It sounds like it is a deeded ownership. Heirs can refuse a bequest, but that doesn't mean that the real property ownership interest disappears or evaporates into thin air. I'm just speculating that your mother's estate attorney is making you aware that in order to deed back the ownership the estate needs to complete an ancillary probate in Florida. That requires the executor of the estate to hire counsel in FL to complete the legal transfer of ownership from what is now your mom's estate to whomever will be accepting the title. If you are the executor, you cannot simply "wash your hands of it", as you have fiduciary obligations as executor to process the estate and pay the bills and dispose of assets owned by your mom, whether it is her furniture or a deeded timeshare interest.
I'm sure that some folks will simply suggest you abandon the timeshare ownership, but if your mom's estate has assets, you do have an obligation to properly probate her estate. Hiring a lawyer in FL to probate the estate and transfer ownership to someone at a cost of $4k isn't unreasonable. Have you checked on the resale value? Offer it for free to someone and then you the executor is only responsible for the ancillary probate and not any surrender fee. Of course, much will depend upon the value of your mom's estate and the value of that particular timeshare.
BTW-because all deeded real estate can only be legally transferred by the owner or an authorized representative of the owner acting with a DPOA during the owner's life, that is why revocable living trust ownership is encouraged for real property. When deeded real estate is owned by a revocable living trust, and the grantor of the trust dies, the successor trustee legally steps into the shoes of the original trustee and is able to legally convey real property ownership interests without court intervention. When real property is owned by an individual who passes, the only way to legally transfer ownership is to probate the estate. Real property probated in a jurisdiction where the decedent did not reside is called an ancillary probate. The legal transfer of ownership after the death of the owner requires the probate court be involved.