I was notified a MSB told a teller they cash paid a check for a friend for over $10,000.

Because this is a small mom & pop shop, I'm guessing they haven't filed a CTR on their friend (even though I have provided documentation to them about the requirements of a MSB).

Is it my responsibility to make sure this CTR has been completed?

No, but if they are engaging in activity that would require CTR filing, part of your due diligence might involving making sure that have BSA/AML procedures in place.

We maintain a Anti-Money Laundering Certification Form in all of our MSB files to ensure they have a Money Laundering Program to include CTRs, SARs, etc.