We just want the smooth shine back of our marble?

My husband cleaned a piece of marble (with a camphor root growing through it) with electrode prep pads that are alcohol with a small amount of pumice.  It has little circles in the sheen now (as opposed to the couple grinding circles left from the original preparation).  It was never perfect, and we just want the smooth shine back, not all the flaws removed.  Would raw leather work on this? 

Thanks,
Erin.