Basement half wall

I'm interested in dividing part of my finished basement by building a half wall (between 36-42" tall). The half wall will span aprox. 8.5 ft across and will be attached to two existing walls on both sides (fastened to studs in these walls). There is existing wall-to-wall carpeting, on top of a concrete floor.

I realize the optimal thing to do is to cut the carpet, secure the bottom plate to the concrete floor, attaching both sides of the wall to the adjoining walls on both sides, and resecuring the carpet on both sides of the new wall with new tack strips and restretching the carpet properly.

HOWEVER, I'm interested in keeping this wall relatively easy to remove in the future. I'm concerned that a future buyer may not like it, so I'll want to remove it before or after listing the house in the future. Given this is just a knee wall without any need to support anything, is it feasible to build it on top of the carpet? Otherwise, the whole carpet would need to be replaced if the wall was ever removed in the future. (I realize this is generally not ideal, but don't want to over-engineer something that is potentially temporary)

If I go this route, what's the best way to secure the wall to ensure it's not wobbly? Should I attempt to still fasten the bottom plate through the carpet to the concrete floor in a couple of spots? For extra security, I could potentially lag bolt the wall to the stud on the adjoining interior wall. The other stud is on an exterior wall, so I would probably only be able to fasten to that wall using screws, not bolts.

Any thoughts or general recommendations about this process?