That cursor thing is odd, I can't fathom how that could be related. Can you post a video or something so I can show support?
It does look like your probe is just picking up ambient noise, some tricks to help reduce it would be to 1- try a new environment and 2- try changing the orientation of the probe cables and see if that helps.
Can you also run an FFT and see if you can identify a noise frequency? Might shed some light on the situation.
It IS quite weird. I did some more experiments and noticed that sometimes I even got two little ghost blips that move in opposite directions and that they don't move at the same speed as the cursor. Depending on how my horizontal is set they will move further across the screen than the cursor has moved.
Here's the best I could do by pointing my phone at the screen.
You can see two blips moving in opposite directions on the left and the cursor on the right.
10X probe connected to the probe comp.
https://1drv.ms/v/s!ArYn6kcDECISkRY7WS_erYNxklZ8This .mp4 won't play in a browser for some reason so you'll probably have to download it first.
I know Dave did a video quite a while ago about how people keep saying that digital scopes are noisier than analogue ones even if it's not true. I was still surprized at what the trace looked like when I was trying to measure an 18mV signal without using BW limiting and high resolution mode.
It was the same at someone else's house (but in the same village) and moving the probe wires around makes the noise worse most of the time.