In an appointment type form, can I get rid of an option once a user chooses it?

We do not have reservations with time selection but the following might be of help.

You can use the date reservation widget https://widgets.jotform.com/widget/date_reservation, the only downside is that it does not have time selection.

Or you can use the gift registry widget where you could list the items and add a limit.

https://widgets.jotform.com/widget/gift_registry