Perhaps Nixy calls it Timby's pet rhetorically. After all, Timby doesn't appear to care very much for it in the fifth panel.
But maybe it is Timby's pet, and he doesn't care much for it anyway. Or maybe he cares for it plenty but isn't worried about it, because it is famously resiliant to this sort of manhandlement.
Whatever the case, its presence in their house is distressing, and not to you and me alone - Nixy sure wants it disposed of. And Timby obliges.
"Timby, get your pet away from me! It's making a mess on the floor!"
"Not out the window! There a parking lot down there!"
"Oh well, not my problem anymore!"
SMASH HONK! HONK! HONK! HONK! ...