They will pay you and instruct you to transfer the reservation to their client, not to them.
I have rented through brokers on this basis three time and they were all easy transactions. Obviously the broker makes a profit above what you are charging, but everyone seems happy on these deals -- and there was no bargaining on the price in my cases.
Concierge Realty also shops the Redweek site for weeks for their clients. They then contact the owner/renter.
They brokered a rental for me a few years ago and it was a great experience.
You just have to make sure the company contacting you is trustworthy, and that's the only concern.
Another reason NOT to use the Redweek full service. I won't use that because the owner doesn't get paid until check-in.
I rent out my own weeks on Redweek via "do it yourself", I use a contract, and I get paid upfront and 90% of my transactions
have been "full payment upfront" with no refund option (as long as the resort is open and operable). If the renter wants to purchase independent travel insurance
it will protect them, and I have no worries. Renting a house or a condo is similar----no need to give away any control to the renter.