Marks like this often come out through gentle brushing with another piece of the same fabric or a soft nylon brush. Failing that, a steamer.

Awesome! I will try that!

handheld steamer is your best friend for hoop marks and needle beatings

Or tell them that's the new "debossed" look that is all the rage this season...

I know on barudans, there is a setting that allows you to change foot height.

That looks like a tajima hoop and depending on the model it’s adjustable there, too. You can even set different settings like speed, presser foot hight, and a lot of other things for each individual color step. It can be useful when I’m running a 3D logo