Of course they did. Nowhere does the Constitution give select members of Congress the authority to do what they did. You are clueless about the Constitution to believe that it does.

Furthermore, their actions could very well be in violation of U.S. law (the Logan Act).
Re: the Congressional letter to Iran...
1. there was no violation of the Constitution
2. there was no violation of the Logan Act
The President has lost the confidence of much of Congress, and much of the American People, with regard to his conduct in the sphere of foreign policy.
The President is no longer trusted to do the right thing -
especially in matters related to nuclear weaponry in the hands of mortal enemies.
There's too much at stake to leave this to Neville Chamberlain types.
Congress cannot stop the (now, somewhat distrusted) President from negotiating a bad deal.
So they openly and clearly inform the beneficiary (Iran) of any such pending bad deal that the deal will be renounced, the minute the President leaves office.
It's unprecedented alright, or, at least, highly irregular - and more than a little uncomfortable for most Americans - but those elected representatives and integral and fully-empowerd members of the Government (the branch that passes judgment on and ratifies treaties, by the way) decided that the situation had deteriorated to the point where such an intervention was necessary and appropriate.
Checks and balances - under extraordinary circumstances.
The Constitution still works... checks-and-balances are alive and well... inside and outside of a formal legislative process.
The letter-signatories broke no laws.
If you believe differently... wake us up when the US Justice Dept delivers indictments against the letter-signatories, for breaking the law.