Is this actual insulation material or something homemade?

It's "Comfort-Therm" R-19 formaldehyde-free encapsulated batts. The joists aren't 16" on center so the batts are sitting somewhat loosly in the cavities.

As described, their only function is to take up space. If you want them to serve another purpose, further information is needed on what that purpose is.

Here is a link that might be useful: Comfort Therm

I don't expect that it's providing any insulation, I'm just worried about moisture hence mold build up b/c of the insulation.

Basically I want to know if I have to tear down the panelling and drywall and remove the insulation.

As long as basement relative humidity is less than 50% in the summer, I wouldn't be concerned at all.