They send back their own message in the same format: a timing signal, on top of a copy of the alien's first digital signal. Then their own faster digital signal containing the specifications for the radio bands and encoding which Emergency Services use. And then finally some analog audio and an accompanying black-and-white video.
This is not a choice made extemporaneously — Emergency Services usually has far more likely scenarios to plan for, but there is no force that would have stopped them from having procedures ready for a scenario like this. Matching the format of the signal is one planned method to communicate that they have received and understood the message.
The message they send shows three humans, wearing matching diplomatic uniforms. The deep purple doesn't come through on the video, but their enthusiasm does. The figure on the left is crying. They can't help it.
The middle human reads off a prepared message — once in Larger Continent Trade Language, and once in Smaller Continent Official Language. She knows that it will not be understood — but the aliens will surely save the message, and it will be these words that go down in history as þereminia's first message to their neighbors from the stars:
"Welcome. To one who has come an incredible distance: we[ex] convey earnest greetings in the name of þereminia and the people who call it home. We[ex] look forward to establishing peaceful contact and mutually beneficial trades between our[in] respective civilizations."