Who was the eBay seller? If it was one of the larger resellers (tochoa, timeshareconsultants, etc.) then they will have their own captive or preferred closing department and you won't have any choice over the closing company. They are generally efficient and competent, so I wouldn't worry about it. If you bought from a private party and the closing company isn't set, LT Transfers is a great, low-cost option. https://www.lttransfers.com/
But do you want title insurance? You're probably paying a fair amount for this week, so you might want to have that protection. Others can opine but I don't believe you can get title insurance through LT Transfers. You might need to go through a title company. Fidelity and First American have timeshare programs.
If Marriott exercises ROFR it will cost you nothing other than your time and effort in putting together the purchase agreement.
Make sure you have the seller request two estoppels from Marriott: a usage estoppel (tells you what unit, season, etc. the week can book) and a financial estoppel (tells you how much the maintenance fee is, how often paid, and whether it's current). You want Marriott to tell you what you're buying, and not just trust the seller.