If you included the make, model and serial number of the revolver in your letter, then they traced the revolver to you by contacting the maker, the wholesaler, and the retailer to obtain the information. That is legal under current law.
It would be illegal if they could put your name into a search engine and the revolver popped up.
There is an exception. There is a law requiring sales of more than two handguns in a week to an individual be reported on a special form. That was done *before* Congress forbid establishment of a national registry. Those guns are in a national database, which was grandfathered in.
In 1983 I did provide the make, model & serial# to BATF because I no longer had the bill of sale which would have sufficed to re-import the gun.
They took that & provided me with the date of purchase & address of the store where I had bought the gun. Back to me in three weeks when overseas mail still took a week to get there.
Since this was not part of a criminal investigation but a request for confirmation of ownership, BATF’s speed in replying was pretty amazing for the time.
IMO I think databases existed even then.
Could explain why nowadays “unpapered” guns are sought after.