recessing a part

 From:  Marv (MSWRITES)
7612.1 
I have a .375 part which needs to be recessed .125.
I'm attaching the drawing showing how I'm doing it. I'm sure there is a better way. Can you help please?

1/ I extruded main part -.375
2/ I created separate rectangle and marked over .125
3/ I extruded that rectangle -.25

4/ How can I remove the lines pointed to in LH_side plate_3.3dm.
5/ I hide the rectangle line on the top recess but not on the bottom recess.