Mountain Eagle was actually bluffing, using such a method to put pressure on the female thief...
Because he guessed that the female thief probably didn't even understand why.
There should be no pressure for the female thief to betray her employer now.
It's just that she could see that Selena couldn't offer her the raise she wanted, so she was using Joe to try to gain more leverage to get away with it later.
Mountain Eagle was out of patience because finding the female thief for Selena was his promise, but solving the case entirely was not.
He was on his own to take care of the peripheral security for Blood Fox and his team, which limited his ability to do anything else, but helping Selena had been suggested by Blood Fox...
With the thought that speaking up didn't cost anything, Mountain Eagle helped Selena exert tremendous pressure on the female thief.
His guess might not be accurate, but as long as the female thief harbored doubts, her bargaining chips would devalue.