After upsetting Angela by euthanizing Sprinkles, Dwight traps Garbage and offers him to her as a gift in an attempt to win her favor again. When Angela declines the offer, Dwight releases the cat into a Vance Refrigeration office.
Two weeks later, Andy found Garbage outside Vance Refrigeration and captured him in a cardboard box, which he left on Angela's desk as a present. This time, she accepts the gift and allows Andy to take her out for dinner.
Garbage vs Bandit
It's a common misconception that Garbage is the same cat as Bandit, a cat that Angela keeps in an office drawer and appears several times later in the series. It is possible that the two cats were intended to be the same, however, they look different: Garbage's stripey pattern continues all the way down to his paws, whereas Bandit has white paws.
It is likely that the cats are the same cat in universe, and Angela named him Bandit, as only Dwight and Mose called him Garbage, and Angela is pretending that this cat is coming from Andy as she was mad at Dwight for killing Sprinkles. When Andy gives her the cat she names it Bandit. The cat is only portrayed by different cats from season to season. The show has done this in the past, as shown by their recasting of Pam’s mother between seasons.