Saints Cap Moves: $27,092,090 cap space ….. 8 restructures, 3 extensions, 3 pay cut, 1 release [All current cap moves are in OP]

I think "explore the market" means he wanted to see what his market value was before actually renegotiating the contract, similar to what Stafford and the Rams did. I don't think it necessarily means Carr wanted to leave the team. He might have wanted to leave, but he might have just wanted to find out his market value before doing a new contract.
That's an interesting argument. I can see that.