Im guessing you mean removing the whole post slot from the page? It should be possible. I've seen a script out there before. I think it was written by Grue here if I'm not mistaken.
grue wrote a script to hide signatures with a certain complexity from pages (effectively hiding most paid signatures), but the OP is looking for a script to hide the "This user is currently ignored." text on posts from ignored users.
I haven't used Tampermonkey before, but it would be extremely easy to do this with jQuery. I'll have to look into Tampermonkey scripts, and see if I'd be able to put something together for you OP.
Yes. Grue wrote that script, im currently using it ^_^ how hypocritical of me.
Tampemonkey basically runs a userscript on the page you want, and can edit the appearance of the page and make commands behind the scene. In some cases, people have made tampermonkey bots.