Final answer:
Gregor is happy about his injury because it enables him to help someone else, which in turn gives him a sense of purpose and helps him overcome his own feelings of being a 'lonely outcast'.
Step-by-step explanation:
The passage suggests that despite Gregor's own tribulations, one thing that brings him happiness in regards to his injury is the opportunity it has provided to help someone else who is also suffering. He finds solace in the sense that he can contribute positively to another's life, especially considering he felt like a "lonely outcast" before. This chance to make a difference in someone else's life, to help them to a "happier life", is what gives him a new purpose and alleviates his own pain, providing him with a sense of meaning.