Pest Control – How to Fix Gap Between Carpet and Wall to Prevent Rodents

I'd go ahead and pull it up and see what you've got. It sounds like it's in pretty poor shape so you're going to have to get rid of it either way.

Depending on how the carpet was installed you'll probably find tack strips that look something like like this:

You might also find staples -- I don't know if this is common but our installer used a staple gun in some troublesome spots. Most if not all of the staples will probably be pulled out when you rip out the carpet.

Before removing anything, take a look at the hardwood stair treads and make a preliminary decision about whether you think they're in good enough condition to leave exposed. If they're really rough and/or you want to recarpet, leave the tack strips in place and hammer in the staples.

If you do want to leave the stairs uncarpeted, you can just remove the tack strips, being careful not to damage the floor underneath. For minimal damage I'd recommend this type of prybar available at box stores for ~$14:

Use a hammer to tap the pointy claw end (like you would hammer a chisel) under the head of each nail holding the tack strip down, then pry up the nail enough that you can get your hammer's claw under it to pull it out. No tools ever need touch your stair tread.

I am having a bit of a problem understanding why plaster board or sheetrock would be finished to door and window jams without a casing/molding frame. In the few instances I have seen flush fitting walls to doors/windows, the wall covering is a thin, finished edge panel of some type, not 1/2" rock. In your case, the pic looks like the edge of the was was simply finished with some type of caulk or sealant to the jam, and either the jams have cupped or the caulking has shrunk over time causing the gaps to appear.

My first option would be to case the doors and windows with a molding. This would cover the gaps and secure the "flapping" wall board. The second option could be to use an elastomer paintable caulk/sealant to fill the gaps. I might use some finish nails to tighten the wall board and counter sink the nails slightly and fill and finish the holes. Hint: cover the jams and edge of the wall board with blue painter's tape before applying the caulk. Smooth the caulk into the gaps with a putty knife, then immediately remove the tape, leaving a nice crisp, straight line.