Not an attorney, not legal advice... this is what I would do myself.
GET REAL LEGAL ADVICE.
There are only a few reasons they would want exclusivity.
First, they like it so much, they want it to be brand specific. This should be very expensive for them, especially if your work is well known.
Second, they are in violation of your copyright already and they want to cure it without possibility of recourse.
Finally, they just want to be able to license it to anyone else and they perceive a market for it.
Most likely are first and second.
If you choose the first, make sure it’s worth it to you. Also make sure that any prior use of the artwork doesn’t violate their contract, even if it hasn’t surfaced yet.
If you suspect the second, make sure they disclose, as an addendum to the agreement, to you any prior use THEY have of your artwork, or derivative works, and base your decision on that. Make sure any after-the-fact discovery of their violations by you or anyone else triggers a very large penalty payment, or ends the agreement.
If it’s the third reason, and they see an untapped market, they can’t realize it without your artwork. Build in some ceilings after which you get a cut, or caveats where they don’t control it.
Good luck.<p>p.s. Remember that if you open source it, anyone can use it for anything they want, subject to your license terms, even if the things aren’t things you support. Think about it carefully.