Gavin decided to write a letter to his favorite uncle on Blah Buster Day. He wrote the letter on his computer and printed it on bright blue paper. It took him 31 minutes to write the letter. If he started writing it at 10:33 a.m., what time did he finish the letter?

If it took Gavin 31 minutes to write the letter, and he started at 10:33 a.m., then he finished at 10:33 + 0:31 = 11:04 a.m. Answer: \boxed{11:04}.

To determine the finish time, we need to add the duration of time it took Gavin to write the letter to the starting time of 10:33 a.m.

If it took Gavin 31 minutes to write the letter, we can add this to the starting time to find the finish time.

Adding 31 minutes to 10:33 a.m.:

10:33 a.m. + 31 minutes = 11:04 a.m.

Therefore, Gavin finished writing the letter at 11:04 a.m.