*QUOTED CONTENT REMOVED DUE TO FORUM RULES REMINDER*
Oddly enough, TESS doesn't list any such registered mark.
tmsearch.uspto.gov
The symbol
® should be an indication that the mark is registered - if you are seeking such a registration, you need to wait until it happens before using that symbol. You could use either the symbol SM for it as an unregistered service mark or TM for it as an unregistered trademark. To have any protections, of course, you'd need to be able to demonstrate a use in commerce of the mark. See, e.g.,
https://en.wikipedia.org/wiki/Service_mark for an explanation of how service marks work. Not intended as legal advice, but
https://www.justia.com/intellectual-property/trademarks/strength-of-marks/descriptive-marks/ also provides a discussion of the limitations on using descriptive terms like that as marks and the weakness of any protection that might be afforded them.
BTW, hoarding and selling to the highest bidder seem more like they would be actions taken by a broker or postcard timeshare exit company than actions I would expect a megarenter to take. My expectations would be that those folks would try to get as many high value stays booked as they can at as low a cost as possible, then rent them out at a profit. All indications seem to point to Wyndham cracking down on folks that only rent one stay, so my interpretation might be wrong.