Hi, Kari. The white mark is there because the water has penetrated the surface of the finish on the chair. Depending on the severity, there are three things you can do to remove the white mark. Try the first suggestion. If that doesn't work move on to the second, then the third only if the second does not work.
First, apply petroleum jelly or mayonnaise and let it sit over night. Five minutes will not do it.
Second, put some denatured alcohol on a rag and gently wipe it over the mark. Use very little alcohol at first (just slightly dampened), keep the rag moving, and don't rub hard, just whisk or polish it over the surface. If the mark does not go away, use a litlle more alcohol, but you do not want the rag to be wet with it.
If the stain still has not gone away (and it probably will), put some toothpaste on the rag and lightly rub it over the area.