When felting over any old felt you can use a bitten primer to get a proper fix, some felts are also a 3 layer system allowing them to go over old felt, however if he has quoted for old felt to be removed then that is what he should have done. Any old felt roof needs to be completely taken up and re boarded.
Roofing felt can get wet and still maintain its integrity, as long as it is not exposed to the elements for more than a few days. It will break down in sunlight and with large amounts of ongoing moisture. ... If the felt is still wet, it may rip when shingles are installed.
Permits are required for most new roofs, re-roofs and major roof repair jobs, but many cities don't require them for minor repairs or replacements of less than 100 square feet (one "square") of roofing area.