itrs probaly abestos tile you got there now
leave in place due to contamantion concerns
go over with 1/4″ plywood underlayment, that is what you ask for at lumber yard, secure with 1 1/2 inch ringed flooring nails at 30-40 nials per 4×4 sheet of ply
than put your new tiles right on plywood
leave 1/16 gap in between sheets of ply for expansion, rest is simple cutting to fit
dp