I do not underatand why did you raise this topic "outstanding deportation order" but you sais you have a Green Card ??? Luckily I still do have a Green Card, but INS wants to take it away. What's not clear? Did you not know, you can be US citizen for 40 years and still can be deported?

Luckily I still do have a Green Card, but INS wants to take it away.

But I am actually not even planning to go back home, I will apply being in US. My homeland passport is clean and does not show any deportation.
I guess I have no other choice but keep quite about the order.

I am planning to apply for HSMP from US, and I have an outstanding deportation order in US for overstaying.

Will this order be a problem for UK clearence?

Thank you.