If it doesn't work anymore, using a coffee filter won't recover it. It just removes the crud.
Ihmemies, "Saran wrap" is Elmu-kelmu in Finnish . The purpose here is to make the lousy cap tight.
This is very surprising and XTOL mixed in same tap water (in the same city as Ihmemies) and stored in the same kind of PET bottles has always been fine for 6 months for me. 2-3 months sounds unbelievable. There shouldn't be so much iron here, either.