Giant headset issues

[Veloce]

'Ello 'ello 'ello 

 

What are the ramifications of putting a top headset cup with too small an outer diameter on your frame? Obviously the diameter of the ridge on the inside of the cap lines up with the head set bearing but the outer diameter is too small. ie: There is some frame sticking out around the head set cap.

 

 

 

And if these ramifications are not good, does anyone have a headset cap that will fit a Giant Anthem frame for me, puleeeeeeeeeeeeeeeeez!!