In a vacuum (no moving air), a good 50 mm scope would work. In practice, turbulence in the air will prevent any scope from actually resolving a 7 mm hole. Turbulence-induced blur is almost always the limiting factor at shooting ranges because of the flat terrain and proximity of the observer to the ground.
Still, people often report being able to "see" bullet holes at such long distances. That's possible if the hole has good contrast against the target material. For the same reason that we can "see" stars in the sky that are too small for the eye to resolve, we can "see" high contrast bullet holes in paper at long distances.
You will get the most consistent results using a 50-75 mm scope that has good contrast and resolution. A scope with "HD" or "ED" glass will have the best contrast and resolution under these conditions.
A larger objective will not usually have higher resolution under typical range conditions (i.e., flat terrain and bright daylight). It will see more turbulent air, which actually degrades resolution.
