Sorry for contradicting the expert (BlackC55), but my gaiter and knob come apart. Once the knob and gaiter are removed from the gear lever, remove the cap at the bottom, you will then see that there is another piece that can be levered off. the gaiter will then come loose.
This is certainly the case with mine, but I don't know what car you have. Mine is a manual w203, so yours may be different. In the past I have changed both the gaiter and the knob (at different times).