Companies like that prey on frustrated sellers. They figure you're likely mad enough that you'll pay them a few thousand dollars to take your timeshare off your hands. The problem is that they don't do that. They'll take your money, then list the timeshare for sale (presumably) at an inflated price on a site nobody will buy from, and then they fade into the woodwork. When your unit hasn't sold, the next time maintenance fees come due, the bill comes to you. Those are the "honest" resellers. There are others who will just take your money and disappear.
I don't know what you own, but if the deed is paid off, and you just want to give it away, the best way is to list it on Tug, in both the Bargain Basement forum and on the Marketplace. Offer to pay the closing costs, and maybe even the next year's maintenance fees. You're likely to find a new owner much faster that way. If you haven't offered it that way, it could be why you're still sitting on it. If you don't want to pay those fees, and the maintenance fees come due, you're on the hook for it anyway. It all comes down to how fast you want to be rid of it.
If you're trying to sell a timeshare with an outstanding loan, or for a resale price above what the market brings for your timeshare, you'll likely be sitting on it for awhile.
Good luck!
Dave