Possible GearBox issue? X1 23d AWD

[X1_230d_First]

Hello Everyone, I had posted a new reply on another thread regarding issue that I'm having on my X1 23D AWD. I had Pirelli's on front & Goodyear on rear until last week I had all of them Pirelli.
Now there is weird humming sound that starts when I let the accelerator go off.
I showed it to Kwik-fit guys & they say the noise is very close to the gearbox & suspect there could be a problem with gearbox, this could have been caused due to different tyres & threads in front & back. The gearbox simply got messed up.
Has anyone else experienced such an issue? Are X-Drives such horrible design that minor changes in tyre thread can cause transmission to go bad?
please help