Unfortunately, Book That In doesn't store sent emails at this time, so there isn't a way to find a record of them.
This is a feature that is on our development list - if you would like to be notified when it is available, please contact us on support@bookthatin.com.
If you want to check if an email has been sent and delivered to a contact, please contact support@bookthatin.com and provide the customer's email address, with the rough date/time of sending. We can look back up to 7 days in the email logs to check deliverability, but we can't see email content.