Greyed out Booked Times

This Booking Software has saved me a ton of work, it have been a life-safer in that client’s book right off my website and I don’t have to field phone calls. Saved stress too. Sooo happy with it. ??

PROBLEM:
Clients have been booking time-slots that are already greyed out.
When they hover their cursor over the greyed out time-slot, the time background turns white, and I think they think it is available.

Not intuitively clear perhaps? UI/UX problem?

How can I keep the booked out time-slots visible without clients thinking they are available?

Has happened several times with two clients.

Can you help with that?

The page I need help with: [log in to see the link]