Or simply "Payment required at time of reservation."
I had a big thing to go to this weekend, and I really did not want to go (had fun once I went) but the motivating factor was that DH and I had paid, and by golly, I wanted the yummy dinner!
If we had not paid, I most likely would have stayed home.
It was a buffet, hundreds
of people, and lots of leftover food at the several buffet tables when the staff began clear-away, so not the same situation, but you always want to err on the side of caution.
45 have paid, 60 were invited, what to do? Not admit the ones that have not paid, and No Refunds.
We had table number seating, and had to check-in upon arrival. Some places (wine tastings) do colored wrist bands. Or pre-printed nametags. Or party favors.
"Oh, you came without a prepaid reservation? So glad you are here! Now, please take a moment here to run your card for payment while I find/make/get/print a tag/number/brochure/wrist band/table assignment, etc..."