I was just wondering if using a piece of foil as a shield in  a NEMA head would cause any damage to the lamp.  I wasn't sure if this would redirect the light enough back to the arc tube to cause any kind of damage or not.

If the arctube is not in the center of the circular cross-section of the shield, you are OK.

The rule saying "the reflector should not reflect back to the arctube" mean in fact, then the image projected by the reflector should not be focused back on the arctube. And the only single reflection shape able to focus the image of an object back to the object itself is the circle (or a sphere) with it's center on the exact place as the object. If it's off-centered (by the distance many times the object's dimension, so in the case of 8mm thick HPS arctube few cm off-center is enough), the image is off-focus, so only negligible amount of the energy return back onto the arctube.
For his are sensitive only lamps with vacuum outer, where the dominant arctube cooling mechanism is thermal radiation (so practically only lamps with ceramic arctubes), so the reflected thermal radiation is able to significantly alter the thermal balance. Those with gas filled outer use mainly the convection to cool down the arctube, so the reflected radiation does not alter the thermal balance in any significant manner.

SO just having like a piece that goes around half of the refractor would be ok then?

If you put the shield outside the refractor, the refractor scatter the reflected light enough, so i would not be worried.

But if you want to put it inside, it should not copy the circular shape of the refractor - as it has it's center in the position of the lamp...
But what help is making the reflector sheet as an arc, what touches on it's edges the refractor, but in the middle nearly touches the lamp (keep there at least 1/2 inch), so such arc would have the center of it's curvature in front of the lamp (assume the reflector is behind) and it would be OK again.