Hi Kathy, Sorry Just got back from the hospital my wife had a baby I was with her the hole time.
Saltillo tile is very porous material its just clay. The best way to fix the grout is cutting it out with a 4" diamond blade on a grinder without touching the tile. Then sealing the tile several times first and applying new grout. The other way you would need to get the old grout at least 1/8" below the edge of the tile so you have room for new grout, it can be scraped with manual grout removing tools from local home improvement store and you would need to clean it really good with grout cleaning product to get the oils and dirt out. To apply new grout make sure the old one is damp the new one will stick better. Feel free to call me I can explain more how grout works. Thank you, Paul.

Thanks Paul...................and congrats on your new baby, what a joy! No apologies needed when you were with your woman!
Kathy