The clutch in my 87 BII makes a squeal sometimes when releasing the clutch much like you describe. It is intermittent. Again a new clutch and was pretty much doing that from the start. I first noticed going from 1st to 2nd but have heard it starting in first and between 2nd and 3rd as well.
I tend not to associate that with throwout bearing as it never makes a sound no matter how long I hold in the clutch. I did have a BAD throwout bearing problem once on my 88 BII long ago and it would make noise all the time the clutch was depressed and squeal very bad if held in too long.
The little squeal now I tend to associate with just the clutch releasing like brakes might squeal, but others here are far more experienced than I so maybe I have a similar problem with throwout bearing. It is very minor noise on mine so I am not going to worry. A seriously bad throwout bearing can keep your clutch from disengaging, but I nursed a bad one over 90K miles after first signs of trouble and could have gone longer if the clutch had not worn out. By nurse, I don't mean took it easy on the clutch per se, but rather modified my shifting habits like RonD's comment.
It won't damage anything, just make the noise, and it usually will get worse with use.
I wouldn't ride the clutch, just avoid using it when not needed
Shift into neutral at stops or when slowing down vs downshifting, brake pads are easier to replace.
When my throwout bearing on my 88 B2 started going I heard various pinging sounds like it had lost a couple ball bearings. That was at 95K miles. Somewhere around 105K miles it made a clunk while I was stopped with the clutch depressed. At that point it stopped making noise when I pressed the clutch in, but if I held it in too long it would start to squeal quite nasty. I figured when that clunk occurred either the bearing fell out and it was running on the races or ball bearings seized so it was fixed metal against metal.
I quickly learned to avoid keeping the clutch depressed for long periods doing exactly what Ron suggested to avoid the squealing. Since it wasn't shifting per se but how long the clutch was pushed in, I minimized it by using neutral rather than holding the clutch in. I would still down shift for long hills, but the average approach to a stop, I would slip it into neutral without even using the clutch by just putting a little pressure on the shifter towards neutral as I let off the gas. As the engine load is removed it would slide right out. I would never force it. While going thru gears accelerating, if not in a hurry I would slip it to neutral in the same way and then use the clutch just to sleep into the next gear after a couple seconds.
I never had much problems with it after that. I didn't have much extra clutch pedal movement to disengage the clutch but it was enough. If I loaned the car to someone else they always complain about the clutch not disengaging cause they hold it in and with the constant pressure the margin was lost.
Anyways, I didn't have to get that original clutch/throwout bearing replace until I had 187K miles on it. At that point it was starting to slip. After needing to drive for better than 80K miles like that over like 4 or 5 years I still drive with the same modified habits.
Unless the noise is totally obnoxious and irritating I probably wouldn't worry about it much.
When I was driving aggressively in my Thunderbird a hard 2-3 shift would make a little squealing noise. It turned out that it was the accessory belt. I know, it seems unlikely but it is true.
I've experienced this myself. Change in engine load or something.
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