I've used the shape builder tool to slice off the edge of some lines using a background shape as a guide. The background shape however now has lots of anchor points from where the lines intersected. Is there a way to avoid this or a different method?
As for removing the extra anchor points from the background shape you can select it and go to Object> Path> Simplify.
Or copy your background shape and paste in place a copy. Then lock or hide your original background shape and delete the copy after you have done your shapebuilder.
Or just create horizontal guides and draw your foreground lines to snap to the guides then there is no need for the background shape.
Or simply delete and re-draw your background shape.
I guess these options will depend on your desired final outcome.