Hi Julian.
Slider pins. Do not remove them unless you need to replace them.
Check the fit of the chrome retainer clip in the recess. It should be a snug fit. Look for wear tib and bottom. If there is excess wear then you may need to replace the caliper bracket.
The slider pins should be clean and smooth. They should also be shiny. You grease them by applying a smear of rubber grease or silicone grease to the pin. Just a thin smear.
Clean out the holes into which the boot slides. The hole in the caliper body has a long rubber boot. Be careful not to damage that when cleaning. Cotton buds or paper towel on a dowel with a rounded end. The aim is to get rid if any build up of grease in there.
The boot on the bracket is much smaller and fits inside a groove. The hole for the slider is bare metal.
The rubber boot will swell if petroleum based grease is used. Inspect the rubber boot for tears. Replace if you find any. It should be easy to refit them. If the small boot seems too big to fit the rim into the locating groove, that will be because the correct grease has not been used in the past.
If you have the caliper off the bike and detached from the hoses then practice fitting the caliper and the bracket together, once you have the boots checked and fitted. The caliper should slide in and out smoothly with no sense of anything catching or sticking. It should not get harder as the two parts separate. If it does, that would suggest that the pins are not parallel. Make some allowance for air suction. Maybe check before fitting the boots.
The issue with the grease is that if you apply too much, that slider pin has nowhere to go because the hole is full of grease. Thats an extreme situation. In practice, much more than a smear creates an air lock which tends to blow the caliper away from the bracket, or suck it back. Any excess air needs to be able to fart its way out. Otherwise it can cause the brake pads to be pushed onto the disk.
There is never any need to remove those slider pins from the caliper or from the bracket unless they have to be replaced. But an important warning.....
The early Honda workshop manual (and the one that is commonly available for download), has a serious error in one of the diagrams. The drawing has mistaken that slider pin for the caliper bracket stopper bolt and labelled it as requiring a torque of 69Nm. That is way too much for the slider pin. The actual value is correctly recorded in the tables - 28ish springs to mind - but check for yourself. The figure is different for the two pins, and the 28 is dragged up from memory, something I have learned not to rely on these days. But really, you should never need to undo the slider pins.