These are the rulebook references I was able to come up with. This is from the '05 NFHS book, which I have a PDF of. My current one is at home, but the rules haven't changed.
First of all under Goal Not Counted - this is not listed as one of the items, and it is not referenced under Illegal Stick and Illegal Equipment sections of Rule 5. However there are a couple of situations under the Case Studies that are on point.
Rule 5 Personal and Ejection Fouls
ILLEGAL CROSSE...
5.4 SITUATION D: During the game, an official asks a player for his crosse so the official can check it. Before the player hands the crosse to the official, he adjusts the strings. RULING: A one-minute nonreleasable penalty must be served. If the player with the adjusted crosse scored a goal just before the crosse inspection ("stick check"), the goal is disallowed.
5.4 SITUATION E: A1 scores. Before the next whistle, it is discovered A1 was playing with an illegal crosse. RULING: Goal does not count. A1 serves a one- or three-minute nonreleasable penalty.
5.4 SITUATION F: A3 scores goal by kicking ball into goal. Before the next whistle, the opposing head coach requests an equipment inspection on A3. RULING: If the crosse is found to be illegal, the goal will not count, and the player will serve a one- or three-minute nonreleasable penalty.
There is no citation in the Rules or Case Studies for removing a goal for other illegal equipment, so without that specific citation, the proper call is to penalize the equipment violation but let the goal stand.
Also, the NCAA book has a specific A.R. on illegal equipment and goal scored. The prevailing opinion is if the Fed book does not mention something and the NCAA book does, defer to the NCAA book as backup.
A.R. 13. A1 scores a goal. Before the faceoff, it is noticed that A1 is not wearing a piece of required equipment (e.g., shoulder pads and/or arm pads). RULING: Goal counts, A1 is assessed a one-minute nonreleasable personal foul.
This should serve to address your situation.