How do you delete the dialogue on an Xbox 360?

It's not possible to delete the dialogue on the xbox 360 version, without modifying the game files (which is not allowed and would require a modded console). Deleting dialogue files is only done on the PC version for runs.

Ok so my question is then, how can I submit a fair run off of my Xbox if playing on PC gives an unfair advantage?

PC and Xbox are separated into different categorys. So PC runs don't compete with Xbox runs.

Oh my gosh I am so blind, somehow I did not see that button to change to different consoles. Lol my bad