Q:

What should be done with the "grammar-checker" tag? 

grammar-checker seems a misused tag; in some cases, it seems more appropriate to use grammaticality. 
Should we remove grammar-checker, or does the tag have a purpose and we should write the Wiki page for it? 

A:

These two are the only questions tagged grammar-checker that actually belong there:

https://english.stackexchange.com/q/2993/1547
Microsoft Word's "fragments"

And of those, the first would arguably be closed if it were asked today. 
The other questions in the tag either belong under grammaticality, or somewhere else entirely (judging by all the [closed] questions). 
I think it would be best to remove the grammar-checker tag altogether, because it's not serving much of a purpose other than to confuse people.