My take is that you are probably fine. The odd of being prosecuted because the engraving is not deep enough is probably somewhere south of being struck by lighting.
Assuming this was done via a rotary pantograph type engraver, they probably cant make the existing markings deeper as once you remove the piece from the vice you can never really line up the stylus/trace font again to the prior engraving.
Whenever I engrave folks guns, I always tell them "is this what you want and is it deep enough for you, because once I remove it from the vice that's it" In my experience some folks want the engraving ground super deep where it matches the depth of the factory engraving and others want the bare minimum so that it will all but disappear with alumablack.
Standard copy paper is generally in the 0.003 to 0.004 range so if the engraving is as deep as a single sheet of paper you should be good from a regulation perspective if you want a frame of reference.
Personally I would just leave as is.