Be very, very careful here...
I would never advocate paying anyone to take a timeshare, but it is still true that some timeshares are almost worthless. You may need to "do what you gotta do" if this is something you for which you simply want no further ownership. You couldn't just sell it eBay (or on Bidshares, where advertising for as long as you want is completely free) for even just one dollar???
BEFORE proceeding another step and / or signing (or paying) anything, you really need to first very clearly and very specifically determine and fully understand whether this proposed "arrangement" is merely giving these people power of attorney (which still leaves you as the owner, responsible for all future fees while they try to sell it), or whether a new deed will be recorded in their name now, thereby immediately making them the new owner and making them responsible for any and all future fees.
Please understand that these are two radically different situations and scenarios, as completely different as night and day. Needless to say, the power of attorney approach is (for you) expensive and risky --- you could pay these parasites a thousand dollars and still own the timeshare and all of its associated future maintenance fee obligations. The risk to them is zero, since they have nothing at all at stake and might make a few bucks if they ever sell it. If you couldn't, why would you believe that they can?
I don't know you, or your timeshare or its' value (if any). Nonetheless the words of caution above are sincere. Please make very sure that you fully understand the scenario distinctions described above; failing to do so will ultimately be at your own financial peril. Good luck.
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P.S. I recommend removing your email address from the bottom of your post. Someone in your situation will be perceived as "fresh meat" to some of the many commercial parasites out there looking to take advantage of timeshare owners in a bind. Providing your email address is just an open invitation to hear from lots of them, without the benefit of any "truth test" being applied to their input to you. Make them put all their claims and assertions right here, out in the open, for experienced and knowledgeable TUG members to see, examine and comment out in the bright sunlight...