The video attracted nearly 3 million views on Instagram in the first 24 hours, and created a buzz in Birmingham.
The two reindeer gained red noses in the hours after the mural was unveiled. A protective fence was in place on Tuesday, stopping any other additions to the design.
Mercia Buddle, one of the crowds of people visiting the mural on Tuesday, said it was good for the city.
“Visitors are coming and they have probably come from all over the Midlands,” she said. “And of course it is great to highlight homelessness when the guy was actually on the bench, so it is serving a lot of purposes really – I think it is great.”
Works by Banksy, who has never revealed his identity, have rocketed in value.
A large Banksy painting of chimps sitting in Britain’s parliament sold for more than $17 million in October, a record price at auction for his work.
Later in the same month, however, Banksy opened his own “online store”, selling works for as little as 10 pounds to buyers who were randomly selected and who could answer the question: “Why does art matter?”.