I think what you may be asking is at what point in the weekly water change should you service the filter...yes?
As the others are quick to point out, you only rarely change the media. For a cartridge, you just rinse and reuse until it nearly falls apart.
But just as importantly, you often don't have to touch the filter every week. I'm using a couple of Aquaclear 70's and they typically run for over a month without servicing. The need for service is relative to the number, size and messiness of the fish you have. In theory, some tanks could go for months before a filter really needs to be serviced.
In any event, whether service the filter before, during or after the water change, it really doesn't matter. If you keep the filter running while you stir things up, then you would wait. If, however, you turn them off, you could do it at any point with no timing advantage.