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Unless that particular run is of earth-shaking importance,  I would suggest that you simply toggle off the grid lines in the analyzer software before you run future samples.

Removing them after the fact using PS will take a surprising amount of time and will never give you as good results as if you set the machine up correctly before you started.  Although this is not my field, my impression was that most analyzers store the raw data for each run, and then allow the user to change various display parameters such as start and stop points, horizontal and vertical scales, grid line frequencies, colors, etc. after the fact to produce new plots.  You should look into this possibility.

OTOH, if you can't turn them off because the data isn't yours, then I personally would be concerned with possible issues of academic / scientific integrity and would probably decline to process that image for you.

Tom M