What do you call part of the guitar that the tuning head passes through to keep the tuning head upright?

My brother gave me a guitar one of his friends was going to throw away. It looks like it’s in good conditions, but there are three of these silver circle things missing from the head. They seem to be keeping the tuning heads perpendicular to the guitar head. The tuning heads that are missing the silver circles are being pulled downwards by the strings. What are these things called and do they really make any difference?

It’s just a little bushing. It does exactly what you’re thinking it does.
Here’s some:

http://accessories.musiciansfriend.com/product/Fender-Vintage-Tuning-Key-Bushings-6?sku=361420

You could always buy new tuning machines too, but they’re kind of expensive.

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