Meet and greet?

Hey, I’ve been a sitter on Rover for almost a year. This is the second time a new client reaches out to book and agrees to a meet and greet and then says “heads up I’ve scheduled meet and greets with multiple people” on the same day or this week. The first time this happened they went with the person who they had a meet and greet with a couple hours before our scheduled meet and greet. Bummer but I understand. Now I have another potential client who mentioned the same thing. I responded literally within two minutes of the request coming in. They are interested in booking for two weekends in a row. One weekend which includes Valentines Day and Presidents Day. I have no problem with potential clients meeting with other people. I just don’t want my time to be wasted especially when I anticipate other bookings potentially coming in. Anyone else experience this? Would I be justified to require them to book within 24 hours of the meet and greet ?

Edit: owner rescheduled the meet and greet and has now asked if the price is firm. Seems less like trying to find the perfect fit but instead wanting maybe the cheaper option.