It looks parallel to me.
The series has 3 parallel verb phrases in it:
~ remove the old carpet
~ prepare the surface
~ lay down the matting
The only thing I would suggest is to move "then" to the second verb phrase and then include "finally" or "last" with the third verb phrase ... like this:
~ first remove the old carpet
~ then prepare the surface
~ finally lay down the matting
What is the parallel structure of this sentence? To install new carpeting, workers must first remove the old carpet, prepare the surface, and then lay down the matting
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