I'm experiencing the same problem on an InspIRCd server which also uses +q as owner/founder mode. But not on another InspIRCd server. The issue is most likely that this specific InspIRCd server has no prefix symbol configured for the mode on purpose in the 005 message, even though they use this mode. It is done on purpose to still be able to have +q set while not appearing opped to users in the nickname list, as they are also not +o, so to mingle among the plebs if you will. So its still possible to issue ops/owner-only commands (InspIRCd allows for such a configuration, while other IRCds may require both +q and +o to be set on the user).

This server has: PREFIX=(ov)@+ STATUSMSG=@+

However, InspIRCd does have similar functionality for quiet bans, in the form of a module called "muteban", but it does not implement its own mode, but implements an extended ban instead, of which the syntax is:
"m:nick!user@host" e.g.: /MODE #channel +b m:nick!user@host

Of course, due to how this works, mutebans currently show up in the regular ban list among regular bans.

I also realize that due to how this works and due to InspIRCd's flexibility (e.g. the ability to disable the prefix symbol), it may not be possible to solve this issue cleanly, but wanted to report this anyway.

However, InspIRCd does report this by showing the letter m in the 005 message as follows if the module is loaded:
EXTBAN=,CNORSTUmrz

So maybe this information can be used by mIRC after all to look at the combination of it being an InspIRCd server and it also advertising EXTBAN with the letter m in it, and make the Quiets button work as intended (though this would require extra work/code to split all bans starting with "m:" into their own list), or to simply keep the button disabled and preventing this issue (probably the best).

Just thinking out loud here. smile