Police said a man and woman left McDonald's with a limited edition print from local Newfoundland artist Christopher Peet called "Coming Home" around 11:00 p.m. on Aug 10.
RCMP believe the two are hitchhikers.
After police posted pictures of the suspected thieves online, they received a tip that the duo were panhandling in St. John's on Friday.
"Yes, we know their names, we know a lot about them ... where they're from. The fact that they're backpacking across the country is something that's making it difficult for us to find them," RCMP Constable Rory Jeddore said.
Police said the man, 26, and woman, 23, are both from Alberta.