Calipers for DumMiEs Thread.

The caliper and its support have machine surfaces that the caliper travel on. Those are called ways. From the factory there was a rubber band sandwiched in those ways.
The rubber bands are always broken at the first reline service. Typical action is to wire brush any rust off the ways and apply a little lithium grease.
Any hardware package should include the rubber bands to be complete. If I had them I would install them. Grease works but it collects dust and dirt too meaning more mess to clean up at next reline.