Calcium carbonate and hydrogen peroxide reaction
The effect of aqueous hydrogen peroxide on natural limestone has been examined in a different context (removal of moss and algae from the walls of frequently visited and therefore illuminated show-caves). 

The results were published in Environ Pollut., 2003, 122, 417-422 (PubMed).

The authors exposed etatons of limestone to various aqueous solutions for about four months and examined possible damages using a scanning electron microscope. They found:


  Based on SEM study, the polished surfaces of the carbonate etalons did not show any changes after 135-day exposure to rainwater, 15% peroxide, and 30% peroxide, respectively. No etched pits or any other visible
  effects of dissolution [...] were detected.