Question Regarding Small Amount Of Grass Clippings Under Slab
All buildings (and slabs) settle. The key is to have them settle uniformly. 

There’s several issues 1) type of fill, 2) compaction, 3) maximum size of slab pour

1) You mention adding dirt fill. Generally we use gravel, not dirt. Dirt does not compact as well as gravel. The type of gravel fill is “evenly graded crushed rock”. It tends to bind together good, it settles less over time due to decomposing, etc. Also, install the fill in about 6” lifts before it’s compacted. 

2) Compaction is usually done with a vibration compactor, but depending on what the slab will be used for, you could drive a heavy truck over the fill. (Heavier buildings require better compaction.)

3) Concrete shrinks when it dries. Therefore, you want to pour the slab in square shapes (so it shrinks uniformly and eliminate cracks) and limit the size to about 12’ square maximum. Unusual shapes (like “L” shapes) will cause the slab to crack. 

So, I don’t think a small amount of grass under your slab will be a problem. However, I’d use good construction practices by minimizing fill that will decompose over time and make sure it all compacted uniformly.