Catherine Banning: Damn, I hate being a foregone conclusion.
Thomas Crown: Regret is usually a waste of time, as is gloating.
Detective Michael McCann: I love this neighborhood. Some of these broads are wearing my salary.
Catherine Banning: I would let you in, but...
Thomas Crown: But the world is watching.
Catherine Banning: Yes.
Thomas Crown: Besides, you haven't got any furniture.
Catherine Banning: Oh that's good.
Thomas Crown: You look wonderful!
Catherine Banning: Thank you! How are you?
Thomas Crown: Popular.
Thomas Crown: Do you want to dance? Or do you want to DANCE?
Catherine Banning: Do you really think I am going to sleep with the man I am investigating?
Thomas Crown: Here's to the fear of being trapped.
Answer: I believe that the Monet that Crown hides in his study is not the one that was stolen, it is a copy that he already had prepared. He can enjoy the copy knowing that the original (with the broken spreader bars) is also in his possession. The stolen original then goes to the forger who repairs the broken spreader bars, and then paints another painting (using water soluble paint) over the Monet, so he can "return" it to the museum 3 days later. It gets more complicated when he discovers that Russo is on to him so he has a second forgery made (even the edges forged to match) over the top of "Dogs Playing Poker." He doesn't know if it will be necessary, but given his research into his new adversary, he concocts this contingency. It is likely that he has many contingencies in place, but the "Monet with a ghost underneath" is the only one we get to see. Of course for my theory to hold water, there must be (or have been) that earlier forgery - unless it has been destroyed.
It's not the forgery that he takes out of the briefcase. Even if it were, he still put the Monet in the briefcase at the museum and would have had to break the frame to close the briefcase, thus also breaking the paint and tearing the canvas. The real answer is that it is just something that couldn't really happen, and the movie people don't want the viewer to notice.