I think there could probably be a more informal way. My only point is that sending a message to the other chamber would be the prerogative of the House of Commons, but I think there may be a more informal way, perhaps through the chair's writing a letter as instructed by this committee. That would be a decision of this committee.
Evidence of meeting #148 for Health in the 42nd Parliament, 1st session. (The original version is on Parliament’s site, as are the minutes.) The winning word was senate.
A video is available from Parliament.