When I started seeing my now husband he told me that a policeman friend of his (without his asking or knowing) had run a check on me! I really get where you're coming on feeling the infringement here, I remember feeling insulted that this guy even thought I was worth checking up on (& I'm fairly sure it was illegal to use police records in that way).

In my case it didn't affect my relationship because my then boyfriend did not ask his friend to check me, he had no suspicions about me, plus also he disclosed to me what his friend did which I saw as a positive. If your girlfriend told you about this I would see this as a positive sign, your relationship is with her not her family & friends. By all means be aware of it but I wouldn't let it spoil what you have with this woman - maybe you'll look back and laugh, tbh I do laugh now about this policeman friend (who he no longer even sees these days).