Here's what happened at the end.
I went in and spoke with the owner. Turns out that the screw was not that deep, so it did not penetrated the tire. No patch needed, owner said that if the tired leaked anytime in the future they would take care of patching. Owner offered me a a free oil change with the best german engine oil. I choose a $100 discount on my bill instead. German swedish auto took care of me.
Here's the pics of the screw compared to a quarter.