Compressing a piston to change energy

[Sara Bakhsheshy 2B]

Hello,
In class, we discussed three ways of changing the energy of a system. One of the ways was to do work on a system and we used the example of compressing a piston on a closed system or moving the piston out to do work on the surroundings. Can someone explain this concept to me? I'm just still a bit confused about the relationship between compressing the piston and the energy of the system and surroundings.
Thank you!

[Isabella Torriani 2L]

The piston moving down causes the volume of the space to decrease, and during the compression the momentum of those molecules is increased because they're bouncing off of each other at a greater rate due to the compressed volume, and then the energy increases as a result. Because we are doing work on the gas molecules by compressing the piston, the internal energy increases.

[Mari Brielle Mailed 1B]

I have a follow-up question:

Isabella's explanation helped me understand the change in the system's internal energy. Thanks to that, I get why the system's internal energy increases, but why does the energy of the surroundings decrease after a compression?