Are cut and paste of records from a table to another a correct pratice?
As a general rule I would recommend updating/creating relationships instead of copying data around to different tables.  This is more in line with the relational model, and prevents tables-as-business logic which is what you seem to be doing.

Instead of copying data from one table to another I would think about updating a status flag.  This could be a simple boolean value or a FK relationship to a status table when there are more than two possible states.

Depending on your business logic a better solution would probably be to associate a user with their selected tasks.  This could be via a join table or with a nullable FK on the BookedTasks table.  

To give a better or more complete answer I would need you to update your question to include your proposed table structures and some sample data/workflows.