Solution as suggested by
Dan_Patterson
I took a look at the attribute table of the contour layer, inspected the length of the contours and - by comparing with my dem that I have already classified and altered according to my needs - which values could be deleted. Using the selection tool I selected those below a specific value and created an extra layer with only those contours remaining that I wanted to keep.
Needed to do that quite carefully since there were some peaks that I wanted to keep, did the selection tool with the additional condition of regarding the contour value so that mountains would not vanish, but besides that this worked fine!