My basement was partially finished by previous owners. The walls are 2x2 strips attached directly to the poured foundation with cheapo luan paneling overtop and no insulation. I hate the paneling, and want to insulate anyways. I think I've got a pretty good grasp of the normal basement insulation process (XPS foam attached to the wall with 2x4 wall in front of it). Wondering if I need to completely remove the existing 2x2s and insulate the whole wall, or can I just put the xps between the existing furring strips and then drywall (or put another layer of foam) over that?
Unless it is PT wood, i would remove the strapping. Untreated wood should never be on concrete, it will rot more quickly. HD has the 2" pink stuff with notches at 24" for surring strips. Screw the furring strips thru the foam with tapcons to secure the foam and you can mount the drywall to the furring strips.