Do It Yourself

Are you sure it’s a carbon filter? You can try washing it to get the grease out, most of the kitchen filters I’ve seen aren’t carbon but instead a mesh weave of metal. You can likely find a carbon filter that would work online, or something bigger and cut it down to size.

If you find charcoal "pellets" in bulk, you can try and refill the casing.

I once tried carcoal for aquarium water filters, but it was too fine for the casings. The result was a black dusty mess.

But you can usually find no-name filters if you search for the fan model number and manufacturer.

Edit: Oops. This reply ended up in the wrong post somehow. I replied to someone that repaired a washing machine. Or so I thought anyway.

Good job! It feels really good to fix something and not having to spend a fortune on a professional repair or buying a new one. A general and probably obvious tip: take loads of pics before and during taking stuff apart. Even if you fail to repair something it is much cheaper if the thing is not in pieces when the pro arrive. They may even refuse to work on it. It's hard for them to know exactly where else you have put your greasy mitts and messed stuff up. They are responsible for the repair and if someone else has been tinkering with it before, they have to test everything to make sure it works. (If they are good at their job.) That can turn a simple repair into something that requires you to be sitting down when opening the bill. Again, not saying you shouldn't repair stuff, but know what might happen if you fail. No pressure. 😃

If it's electrical and you're not absolutely sure of what you're doing, don't. Changing an outlet or a broken switch is not rocket surgery, but be VERY sure that the power is off. Test twice that there's no power. If you don't know how to test that, you are firmly in the "don't do this" category. It's not hard to learn, so take your time to do that first. Do not modify an existing installation in any way. Leave that to the pros.

Fixing powered appliances, especially washers and stuff like that is extra iffy. Be very careful to get stuff back the way they were. Not saying it can't be done safely by an amateur, but the stakes are considerably higher when there's water and electricity in close proximity. Things can fail in rather "interesting" ways. Don't do anything fancy if you're not absolutely sure about what you're doing. What OP did should be relatively safe and many things aren't as hard as one might think at first glance. I think OP has the right attitude and many things can be fixed for much less than what a professional would charge. But be very careful with electrical stuff and do a lot of research on safety and be sure you know that what you are doing is correct before messing with stuff that can kill you or burn your house down.

I hope I don't come off as wet blanket regarding self-repair. I think that the right to repair is super important and more people should repair their own stuff. I also think we should try to buy stuff that is repairable whenever possible. If you start to repair stuff yourself you will also start to appreciate when stuff is well made and start to look for it. It is also very possible to get your hands on something good for cheap that just needs a (hopefully cheap) repair to be as good as new. It's not for everyone and it takes experience to know when it's a good deal. Reparability is in fact essential to save the fucking planet. Can't just throw shit away and buy new all the time. It's just not sustainable. There are powerful economic forces that don't like repairs at all and do everything they can to make it as hard as possible to repair stuff and make stuff that breaks or become obsolete after a few years. They do not want to make stuff that lasts forever. The whole system depends on that, in fact. There are exceptions, but they are few and far between and are often quite a bit more expensive. If you have the good fortune to be able to afford those products, buy them. Not everyone is so lucky of course, but if we create a bigger market for good quality and reparable stuff, in time the second hand market will grow and then it might be possible to get good stuff for less. A surprising amount of stuff can in fact be repaired with a little ingenuity and pherhaps a cheap 3D printer if you wanna get fancy, but that is often not nescessary either. You can get very far with just common, easy to get stuff. Repairing your old stuff is in fact an act of rebellion against the current economic system. Fight the power! Down with the... Sorry about that. Won't happen again. The people responsible have been sacked.

Unfortunately there are some downsides. Modern appliances typically use a lot less power than older ones and may even pay for themselves in time. Unfortunately, again, the new ones are often a lot less repairable and not built to last. I don't really know what the best is here, but I do hate to throw stuff away that can be fixed, even when it's not economically advantageous to do so. I usually tell myself that it is probably advantageous for the planet in the long run. Be smart about it, I guess? Best thing would be to change the economic system we toil under, but that's for another post. Bit of a long one, this.

TL;DR - Stay safe out there, and follow OPs excellent example.

How to clean heavy caked on grease:

grease is a type of oil aka "non polar liquid". A light grease (like veggie or olive oil) can dissolve it over a long period of time, or you can scrub it off using any kind of abrasive doused in the light oil. After there is nothing but light oil left, rinse it off with water then soap and water. Easy peasy.

How to refresh a activated carbon filter:

You dont. The requirement is to make a 0 oxygen environment and heat up some carbon in a kiln in that environment. There are some stand alone "air purifiers" that you can get from homedepot, but as you say "filters are the printers ink". Some really high end filters like "bunny farts" or bunny air or something use Granulated Activated Carbon (GAC), but most of the cheap ones will take activated carbon dust and make it into a wet slurry and spread over a sponge the size of your filter, so you technically have activated carbon. Good luck on getting a cheap replacement.

@whaleross granular activated carbon for fish-tank filters is relatively less expensive - though you might be able to make your own charcoal with a fire-pit and have as effective material. Your stove hood filter probably has some kind of metal-framed and non-serviceable assembly - which could maybe be disassembled and "refilled". My vent hood filter appears to be a black piece of felt - questionable whether it actually contains carbon or not, tbh. I'd probably eventually replace it with metallic mesh in a multi-layered arrangement and not worry about carbon at all. The main role is to trap grease, not odors.