After this quick scene, the creature is never mentioned again. So one of two things must have happened:
Option one: Peter Parker stomped this thing to death in his civilian clothes. Unless Peter decided that he didn't want to ruin his jeans with radioactive rodent blood, a normal-looking teenager slaughtered this genetic abomination with his bare hands. I don't know if there's anything in history that could take away the magic of Spider-Man more than the sentence "And then Peter Parker crushed the spine of this victim of biological tampering." Then again, the famous Spider-Man theme does include the lyrics Spider-Man, Spider-Man. Does whatever a spider can. Save the day? He'll do that. And mercy kill your mutant rat.
Option two: While the hideous blend of CGI and a tired character designer is trying to lizard-ize Manhattan, there is a gigantic lizard-mouse running around. The former will become the norm. Every week, some new animal-themed megalomaniac will menace the financial district. But how does Spider-Man deal with the latter? Grab a mouse from the pet store and wait for it to come sniffing? Follow the trail of people who have been attacked by a huge lizard-mouse? That's way more horrifying than anything any other Spider-Man villain could accomplish. Doctor Octopus will rob your bank. Green Goblin might yell from the top of your bridge. But in this case, you're going to have to explain to Spider-Man what gnawed off your hands and what direction it went in.