yes, when re grouting tile, it is best to remove all the grout down to the green board or what ever you have. I use a scraper and a dental tool to get it all out.
I have good luck with pure bleach poured on the grout and let it sit. If you have trouble with the bleach rolling off, saturate bleach in bread and mold it on the areas.
After the grout has been cleaned and cured, apply silicon sealer and the cleaning will not be so difficult in the future. Read directions carefully when doing this.
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