“unsolicited mentions” are just that - mentions or replies that a user did not explicitly solicit (i.e. opt-in for, request or otherwise expect to receive).
As we’ve discussed elsewhere in these forums, we are unable to describe our antispam and safety algorithms in detail, but here’s the general concept covering this case:
If an app is sending lots of automated responses to users who didn’t directly interact with your app in the first place, this is likely to be annoying to them, and may cause the app creating these Tweets to be write-restricted until the behaviour is corrected. If an app is only sending mentions, that’s potentially another signal that this behaviour might not be wanted. Beyond that, if users mark or report message from an app as spam (unwanted) then this might be another signal.