Scratched Spindle

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Good Evening Ladies and Gentlemen,

I noticed this afternoon while turning between centers i have a scratch inside my spindlenose right where the MT sleeve sits, I must have had a little debris between the sleeve and it spun in the bore, i an thinking about lapping it with crocas cloth on a round sided wooden stick to lap it out, before i do so how would you do it?

Thanks in Advance,                                    

Anthony.