That "green stuff" can be one of many things. It might be algae, or it could be a type of plant - or, it could be a combination. I've learned never to make assumptions.
More than likely, you're referring to a type of filamentous algae (many species exist).

However, duckweed and/or watermeal also fit the description of "green stuff".

Basically, if the "green stuff" is a type of filamentous algae, odds are that CUTRINE PLUS will help keep it in check with periodic treatments. But, nothing (legal) will get rid of it (permanently or long-term).
Unless you have some pictures of the green stuff from last summer; or unless you can positively ID it from these or other pictures, we'll need to wait and see exactly you're dealing with before a management approach may be suggested (which might include other options besides or in addition to chemical treatments).