This could be a problem. What I suggest is that you boil some water in a shallow pot/pan and sponge-wash the tile. Try keeping the how water off the existing grout. You may have to repeat this a lot of times until it is gone. Don' scrub as you may scratch the tile. Just keep the sponge slightly saturated with hot water. Use rubber gloves. I did this every time (I was able to) when my wife boiled water for hot tea. I used this method to remove a ring.
No promises but it's worth trying. My best to ya and hope this helps.