I need some help understanding the schematics of DIY HS102 oscilloscope
I agree that the 1.2V regulator's output is not used, even on the drawing of the prototype board there's nothing connected to pin 2 (which is the output).

So the LDO only loads the 3.3 V line with it's quiescent current consumption.

I also see no reason why it is there. Removing it should not change anything.

Perhaps the author first thought he needed a 1.2 V and then later discovered that he didn't. Or indeed as Marcus suggests in the comments: the author didn't have a clue and just copied the design including superfluous components.