There are 2 common types of systems used to retain shelf support pegs. One has a center plastic plunger that when inserted causes barbs on the support's base to expand and lock the peg into place (see illustration).

This type can often be identified by looking for evidence of a (now filled) center hollow. To remove these the center plunger has to be pushed right through the support peg using an awl or similar tool, to release the barbs.

The other common type is twisted into place. To remove these, the very base of the peg needs to be grasped with a pair of pliers and twisted. Blunt nosed pliers work best for this when held perpendicular to the refrigerator interior's surface.

Once grasped firmly, the peg needs to be rotated clockwise 90° to release the support peg's retaining wires. After this is done, the peg should be loose and able to be manoeuvred. The loose support may have to be manipulated slightly to align the retaining wires through the 'keyhole' slot it's mounted in. Once this is done, the old support can be removed.

To install the replacement, insert the new part in the 'keyhole' shaped hole and again holding the base securely, rotate the peg 90° clockwise. It should now be tightly held in place.