U.S. Constitution, Art. I, Sec. 6.
Doesn't say anything about a privilege against having your office searched, pursuant to warrant, in the case of a suspected felony.
There is no legitimate constitutional issue here, and the Congresscritters know it.
I agree with you -- in what world does that clause have anything to do with a search warrant served and searching a Congressman's office? As far as I know the bribe itself did not occur IN Session... This is strange indeed. Methinks some people are getting paranoid in DC...