Do you have a workflow in use already for the quality notifications? Do the users get a work item in their business workplace to handle the quality notifications? If yes, then you can use the workflow deadline functionality easily.
Anyhow, if there is no workflow in use, then things might be a bit more complicated (and I could agree with your developer that you might need to develop report to be executed as a background job.
Another option might be that even if there is no workflow in use at the moment, you could check if you can start one easily (=always when quality notification gets created). The workflow could be a really simple one: Just put an email sending step there, and then put a condition (requested start or whatever) that checks whether 30 days have passed, and if it has, send the email. (Of course you need to complete the workflow automatically, if the quality notification has been handled before 39 days.
Regards,
Karri