Why are some chemical dangerous to aquatic environment only?
From some of the MSDS (1, 2) I come across, a major component of thermal grease is aluminum oxide.

Risk Management for Hazardous Chemicals by Jeffrey Wayne Vincoli states in page 101 that aluminum oxide has both acute and chronic toxic effects to aquatic life; it also states that aluminum oxide has a half-life longer than 200 days in water; finally, it acknowledges that the short term toxicity data for non-aquatic animals are insufficient.

From this, the reason thermal greases have special notification regarding to fishes can be attributed to those following points:


The long half life makes fishes exposure to it longer and therefore makes them more susceptible.
We simply do not understand how aluminum oxide effect non-aquatic animals.


(According to Risk Management for Hazardous Chemicals, bioaccumulation in food chain might not be the concern.)