First of all, I'm glad you caught this! You're only human so try not to beat yourself up for this.
The way I see it, you really only have two options, right? You either tell them, or you don't. If you don't tell them and then they find out, you could be blacklisted IIRC (and they may indeed find out during your background check). I think it'd be best to just submit an
Academic Change Request on AMCAS as soon as humanly possible. If it is approved, then AMCAS will update the schools ASAP. See the diction below from their website. Additionally, maybe an SDN Adcom can comment on whether it is necessary to let AdComs know directly via email, update letter, etc. of this oversight.
"Add a school and the associated coursework, if you failed to report the school on the AMCAS application at the time of submission. However, you are required to submit the transcript from the institution that was not included when submitting the application. The official transcript must be received prior to submitting the Academic Change Request. If the transcript is not received by AMCAS prior to submitting the Academic Change Request, it will be denied."