The filter pad should be rinsed with each weekly water change (using tank water) to clear off gunk. It's important to use tank water, as tap water has chlorine which will kill the beneficial bacteria.
The only reason to replace a filter pad is the activated carbon will only last about 4 weeks, at which point it needs replaced. Some filter brands make it easy to dump old carbon and put new in without throwing the pad away. The spongy pad serves two purposes, one is it provides lots of surface area for beneficial bacteria and the other is it catches free floating particles in the water to keep it clear looking (this is what you are rinsing out).
Because of the beneficial bacteria being in the pad, it's best if you can keep it until it literally falls apart on you and only change the carbon once a month. A lot of filters however come packaged together in a way that you can't easily change out the carbon, in which case you have no choice but to toss the whole thing and replace once a month.
This is less of a problem in an established aquarium, as the majority of beneficial bacteria will be everywhere else (mainly the substrate) instead of mostly the filter like in a new tank.
Even easier is to go with a fully planted aquarium, in which case carbon is not used and you can continue to reuse the filter pad for months until it literally disintegrates on you.