Although I've only recently purchased a metal practice mute, I've spent some time finding out as much as I can (both here and through other musicians I know)about the effects on my practice that using the mute will have. I'm now of the opinion that the key word is 'Practice', and that it shouldn't be 'Learning'. I've been using mine mainly during fingering exercises, scales and arpeggios, and for pieces that I'm very confident with.
The huge danger is the way the metal mute masks tonality, string crossing errors and musicality when playing, but I think that as long as you are aware of the limitations, it can be used when these points aren't the main target of your practice sessions. Intonation is only marginally compromised by a metal mute, so if the drive of your practice session is intonation, then a mute can be used with confidence.
If I'm focussing on a particular shift, or anything that I'm going to repeat an awful lot - therefore risking the wrath of my neighbours (block of flats, you can hear everything going on) then using the mute is adequate. I don't want to have half my attention on whether or not I'm driving people crazy, when I'm trying to get something right. At the moment, I'm kind of experimenting with a particular scale, with the intention of practising the shifts involved using the mute, and then discussing the progress and any problems with my tutor, and then going from there. Once I find a level that I'm comfortable with when using a mute, I'll know what to look out for, what useful play I can get when using it.
One interesting comment that I'd come across when discussing the use of a mute, is that it is only a more extreme version of the way that room acoustics can mask errors in play, and foster bad habits. With music, we're dealing with the generation of sound and how that sound is received by those listening - knowing how to adapt your style to the acoustics of a room is part of the experience of learning to play. The mute is a severe example of this, but learning how to use it effectively is the key.
I'm fortunate that, I can play without a mute at any reasonable time of the day, without having to worry about complaints, but will still use it for playing later into the evening. Sorry (OP) that you've had the dreaded 'note' thing - my tutor had a problem neighbour, who actually had some kind of environmental officer from the council turn up at her address, during my lesson to warn her about the 'Noise Nuisance'.
Plus, as mentioned in my other thread, I like the sound with the mute in place
(that's like/interested by, not prefer!!!)