Background check in EU

Hey there, I recently passed the loop for a big tech company in the EU (Barcelona) - I have noticed I sent an older version of the CV to the recruiter, where dates about previous jobs were not as precise and exacts (few months off) - I also didn't list a job that I did for ~7 months because is not as relevant as the others, and wanted to keep the CV to a single page

What should I do - should I tell the recruiter about this upfront? Or wait for the bg check to come?

Thanks a lot!