Nip down to your local bike shop and ask for rubber grease, normally red in colour. take the caliper off, put a wedge or stick into the brake after you've taken the pads out. give the pistons a good clean with hot soapy water. after pushing them in and out a few times then apply a good spread of grease, push the pistons in and out again, job done.

if you really want your best using the bleed nipple at the rear of the caliper. find a small tube that fits on the nipple then open and drain into a jar, pull the brake several times to drain the system. if you do get brake fluid on anything wash it off as it's nasty stuff. you'll need new stuff to refill the brakes

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Plough on