Now that they have requested the room, you cannot add a security deposit. The terms of the reservation are based on when they request, which means you were not asking for one at that time. To do this, you will need to ask them to withdraw the request, add the deposit, and have them request again.
If you have concerns, keep talking to them until you are as comfortable as a pig in slop. Any feeling of unease is a red flag. Ask questions until you no longer feel trepidation in renting to them for three weeks. This includes coming up with a plan for changing linens - you seem to want to do that - or working out a plan and agreement to have them launder them while they are staying with you. These are the details you get to iron out before accepting a reservation.
Good luck.