Here is the link to the serial nbrs/dates on Ithaca's website
The majority of Ithacas had the rolled engraving on the sides of the receivers.
What you also have to find out to help determine worth is what barrel does it have on it ? Vent rib / field barrel. Fixed choke / choke tubes. If interchangeable choke, are they all there, if not what is included.
If it is a primo gun and he is intent on selling it, there are a couple Ithaca devoted forums as well as the standard auction sites.
If you go to gunbroker and do a search using Ith* 37 20* you will pick up the ones that are misspelled as Ithica, instead of Ithaca, 20 ga, 20ga etc.
That mask will work on most, but not all of the auction/listing sites.