That rubber thingy is a folded rubber diaphragm that allows the level of the fluid in the reservoir to change without creating a change in reservoir pressure that would prevent proper master cylinder function. It’s main function is to prevent the hydraulic fluid from absorbing moisture from the air.
It’s supposed to be installed with the rubber part folded up into the cap and the reservoir filled.
Each time you pull the clutch or brake lever, you pump some fluid out of the reservoir, each time you release the lever, the fluid flows back into the reservoir. A little hole in the reservoir cap lets air in and out to equalize the pressure in the reservoir, but without the diaphragm the fluid will absorb moisture from humid air. As the fluid absorbs moisture, it’s boiling point drops and vapor bubbles develop that cause brake fade. Obviously fade isn’t an issue with clutches but the moisture in the fluid will still corrode metal parts that come in contact with it.
So like any diaphragm, you don’t really need to put it in, but there may come a point when you wish you did.
