the website was registered in June. Their website is pretty slick looking, but I like to see sites where the principals identify themselves with a photo, name, and their experience. The very novelty of the registration date would be enough for me to disengage with them.
I'm not feeling this. You can ask to see the contract before you sign a letter of intent. If they won't let you see it, it's a scam and they'll use the LOI to try to intimidate you into paying their upfront fees. If they will let you see it, bear in mind that by their nature, scammers don't comply with contracts anyway. They will eventually ask you for some sort of fee up front for one excuse or another, and if you hear from them again after that, it will be under the guise of a different company offering to assist you in getting your money back. Another upfront cost lost.
Ask yourself how they knew what timeshare you have (if they knew), and what made you the lucky special person they called with this wonderful offer.