[MargaretR]

I have found that cats will try to dig under any closed door to escape confinement.

To avoid damage to floorcoverings, use a room that has vynil or lino. Or place a piece on the carpet under the door entrance-- they cant get a clawhold into that, so can't cause damage to it.
The only other way is to put them into a pet transporter cage/box for the time you need them to stay put