Oh Mika, you're doing it all wrong. My cat Fergus says to tell you that the mouse/bat/rat/rabbit should always be very dead before you present it to the humans. If you can also behead or disembowel it, that's a bonus, but not necessary. Fergus also suggests you try hiding the gift under a bed or in a shoe, as the opportunity presents itself.
 

Mika: Tell Fergus Mika does everything right. Fft.
 

Oh, the wee bit mousikie!

The "catching glass," eh? You have a glass kept on hand, dedicated to the purpose? Because, once a glass has had a mouse inside it, you could never actually drink anything from it ever again, even if it had been sterilized in Mt. Doom, never mind the dishwasher? No matter what any persons, who apparently have no sense of disgust, will try to tell you.

Ahem. Not entirely coincidentally, my cat Boyne notes that mice are indeed very good fun, but the toads who sneak into the basement aren't worth the trouble of chasing and may be left for the humans.
 

We don't have an official catching glass, in fact, we just grab whatever's handy and then dishwash it. It is an elected position rather than a permanent title. But that would have been less amusingly succinct.