Toss the old filter water. For mechanical filtration, typically sponges, you can spray/rinse/clean with tap water. For bio-media, you simply rinse with tank water. You can clean the inside of the canister.
Remember, there's far more beneficial bacteria in the substrate and decor of the established tank than in any filter (doubts...consider the available surface area!).
You can do that, my point is that with mechanical media, you don't need to be concerned about protecting beneficial biology...so you can put those sponges under a power spray with tap water and it's fine. What you want to protect is any bio-media that you have in the last trays. Now in my case, I have all my filters totally filled with sponge material...however, I have a well with no chemical treatment so I clean in my kitchen sink with no issues.