Agree with Tony to continue using the well water with a dechlorinator that neutralizes metals like Seachem Prime. Filtered city water might be OK; but if over filtered and similar to R/O or distilled, it might do more harm than good.

For the transfer, would just check pH and temperature is the same. Then capture the frogs in a small plastic container or plastic bag (use a net to guide frog in) and use that to move to new tank. Good luck !