Insulation should befoam-based, i.e., no fibreglass.

Of course, if the rest of the wall is stuffed with fibreglass, it won't be of much help.

Foam based insulation is a poor investment, especially in a small remodel project. You could use Rockwool which is water resistant, but using fiberglass makes more sense in this situation. Just stuff it in...

No way I'd use anything other than a closed-cell foam in a basement-- I think ksc36 must be thinking spray foam for that comment to make sense, but rigid foam panels cut to just fit the stud bays is what I'd use in that situation. Better to run them continuously behind the stud wall, but too late for that.

Years back we had flooding in our basement from an overload of rain backing up the storm sewers. A nightmare! We were advised to replace 4 ft if the wallboard as it would be less labour to install whole wallboard sideways (they are 4x8 usually). We also had the pink fibreglass behind, and while it looked and felt dry, it was sopping wet. We swore we would make the repairs as waterproof as possible, so we went with the spray foam insulation, professionally installed. So our upper part of walls are fibreglass and lower is spray foam. (Luckily we did have vapour barrier, though). I highly recommend tie spray foam and wish we could do the whole house in it.

Unless the OP guts all the exterior walls, only the bottom 25% or so would have the foam. If it was the top 25%, it might be worth it. Insulating basements has very little return, the value is in sealing basements.

Thanks everyone, these are helpful comments. If I went the foam board route, I could pull out what’s left of the insulation and push the foam boards in as best as I can. I would have to piece it together because I can only fit so much height in the opening. I’m sure this Diminishes the value of having the foam in the first place, but maybe it’s worth doing this if it will offer more protection against mold. Thoughts?

Unless the boards are tightly sealed and firmly adhered to the foundation wall, they're of little use.

On new construction, we had a cold floor on a bathroom over an entry. We placed layers of XPS, but not sealed. It didn't work. Same principle applied in living space over a garage. It all met Code, but embarrassingly ineffective.

As ksc36 says, it's hardly worth the effort to properly insulate the bottom quarter of the wall. Meanwhile the critical top portion is problematically insulated.

I would look into a product called Dricore! It's great to solve the issue first though. So figure out how you can minimize water in. Dricore is great going over concrete and then putting a finished product overtop of it.

We only have insulation on the top 3' of our basement. I guess it depends on your climate, but it works great for us.