Unless their processing is very weird, that shouldn’t be the issue.

You send a pulse and record the output of a detector to listen for the reflection. If the laser is reflected at the plume, you should get some pulses very quickly, but also faint and spread out in time, which you would be able to tune out. And the real response from the ground should be more narrow because it’s reflecting at a single distance.

If very short range noise influences the signal when measuring 30km real distance, you’re doing something wrong.

Laser is angled outwards at approx 45 degrees, I think it's well away from the exhaust plume.

I think it would be unlikely that a plume was caused from 30km away on something with no atmosphere.