How to remove “hidden nonop tag” from line or route?

The term "hidden nonop tag" is misleading.

No tags are hidden, all tags are in plain sight, and any editor can be used to add or remove them.

The longer story is this:

OSM allows you to record infinite detail about something. For example, if you just are interested on anything that people or vehicles can move on, you might say "I am looking at anything that has a highway tag". If you are looking only for major roads you might say "I am looking at anything that has a highway=motorway or highway=trunk tag". And there can be lots of additional tags that modify the meaning but normally the additional tags should not turn the meaning around altogether. You don't want something tagged highway=motorway and then note=not actually a motorway, just a little brick path in my garden!!!. This will confuse applications. Now there used to be a time when people would use construction=yes or disused=yes together with something like highway=motorway to indicate it was under construction or disused; this led to confusion among those who just looked at highway=motorway and assumed that's something where cars can travel. Hence we've now switched to different models of tagging these situations, that do not use a highway tag. If you have a highway=motorway construction=yes it could for example happen that some routing engines disregard the construction=yes and use the road, and others don't.

What the OSM Inspector wants to say is: Here is something that on first glance looks like a highway, building, or something, and there are additional tags that say "no, it isn't yet" or "no, it isn't anymore".