[tzs]

Assume Earth, Mars, Jupiter, and the Sun are all roughly in a line.

Let's call the amount of transmit energy needed to get a signal from Earth to Mars with it having a specified strength at the receiver 1 unit of energy.

Earth to Jupiter would require about 64 units of energy, so from the sender's point of view relaying through Mars saves them a lot of transmit energy.

The transmitter on Mars would need about 49 units of energy to get the signal to Jupiter, bringing the total to about 50 units to get from Earth to Mars.

Whether or not spending 1 unit on Earth and 49 on Mars to relay is actually cheaper than spending 64 units on Earth to go directly will depend on the cost of energy on Mars and Earth.