As a landlord, it's a pain in the ass to enforce things like noise violations on tenants. It takes several documented instances and written warnings to constitute grounds for violating a lease. Calling the non-911 police directly is the best thing you can do when there is a noise complaint (or similar). You should even be able to do it on City of SD's "Get It Done" app. This actually gives the landlord proof/ammunition to get the tenants in line.
If you don't feel comfortable with the gift certificates, you should certainly send them back with a simple note saying something like: thank you but you can't accept. No explanation necessary. But I also think it's possible he may just be trying to offer an apology for the nuisance. I've done this to neighbors around jobsites- even when we've done nothing wrong, I understand it's not fun to be next to a construction site, and appreciate their patience.