How can I create a form with a checklist that deletes things that are selected?

So, I want to create a checklist that when people pick a certain time that time gets cancelled out so no one else can select it. Is this possible?

You can achieve that with Gift Registry widget. You can set dates and time inside of your widget and set number of items to one. So once some time is selected, that options will be disabled for other users. Here is my demo form: https://form.jotform.com/60265745885972 

For dates you can use Date Reservation widget.

Hope this will help. Let us know if you need further assistance.