This can be done by changing MediaWiki:Print.css. On https://nl.wikipedia.org/wiki/MediaWiki:Print.css we have:

ol.references li a[href|="#cite_ref"] {display:none;}

It would be nice though if Cite would give the backlinks a special class to make this somewhat easier (or make them invisible by default?).

The above solution doesn't work correctly for refs with multiple backlinks. But the backlinks can actually be given a class by changing the 'Cite references link one' and 'Cite references link many' system messages. See https://nl.wikipedia.org/wiki/MediaWiki:Cite_references_link_one and https://nl.wikipedia.org/wiki/MediaWiki:Cite_references_link_many. Now we can put in Print.css:

.cite-backlink {display:none;}

Changed to 'WORKSFORME'

Why isn't it done in the extension?

The output, including the layout etc, is totally configurable by changing the system messages (cite_*). Making the extension use a specific layout means making it less customizable. Some people read the printable version in their browser, in which case it makes sense to be able to use the backlinks. So, some sites might want to choose to have the backlinks visible.

(In reply to comment #5)

The output, including the layout etc, is totally configurable by changing the
system messages (cite_*). Making the extension use a specific layout means
making it less customizable. Some people read the printable version in their
browser, in which case it makes sense to be able to use the backlinks. So, some
sites might want to choose to have the backlinks visible.

Then what about pre-inserting some classes but not attaching styles to them?

Created attachment 9793
Adding classes to default messages

Yes, that would make it easier when someone wants to hide the backlinks.

Attached:

Added in r111150