Every time I'm not looking at the tablet, a notification appears on the computer telling me. It's not a fault on KDE Connect. But I think it would be interesting establish patterns of notifications to not show. This could be done using regex. Reproducible: Always
http://nekmo.org/share/bugs/kdeconnect01.png
This is also important from the security standpoint. E.g., I want to make sure that the 6-digit confirmation codes that my bank (Alfa Bank) sends to me via SMS are not automatically transferred to the computer. Otherwise (and the bank is really afraid of this situation), malware can keylog my login and password for the internet-banking website, login while I am not watching, create a funds-transfer order, and the only thing that stops it now is that it cannot know that one-time confirmation code. KDE Connect helpfully supplies it to the PC, for the malware to use.
I'm convinced we have to add some notification filter, but if you are so concerned about security to this extreme, you might want to totally disable the telephony plugin completely.
It's possible to disable notification delivery from the android client now.