Edits after intersection

Context:
I am designing my room. I worked on floor, made lathes. On the lather I have created carpet. The carpet was two groups originally. I have exploded them and give the objects together and intersected them. The carpet copies the curves of lathes (but I have moved them 10m away to make a temporary space). The carpet was created like that: I had one curve of the original carpet. I had copied it and rotated by 90°. Small modifications done and as a result I had two groups.

Problem:
Now after I intersected them, I want to delete some redundant edges which do not look good. But when I try to delete them, there are faces deleted which should not be deleted.

My question is how to work around it to build the lines which will create the faces which should stay, and then to remove the redundant edges (been selected on the image bellow).

I work in SU8, if you do some changes export the file to SU8. Thanks. See attachment bellow the image.

skříň.skp (128.4 KB)

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