Is this a member of the bittercress family?

I have not been able to identify this plant growing on disturbed soil on Pender Island on the BC coast. It seems to like some shade. The small white flowers have 4 petals . One small, 2 medium and the slightly larger one has a few purple lines. I know it is not hairy bittercress as it dies not grow in a rossette. It grows low to the ground and spreads along.

 

It is a Veronica sp.

 

Thanks for answering. It sounds like it is weedy and needs controlling or will take over.

 

I've never really noticed it take over an area, but I suppose some controlling couldn't hurt.

 

Thanks. Good to know that it is not going to take over. I have been fighting several invasive plants and want something low growing that will co-exist.

 

Maybe this one, Veronica serpyllifolia - E-Flora BC Atlas Page

 

Thanks for replying. Yes, a hood choice and not invasive