Reading through the javaFX source code, GridPane's setRowIndex and setColumnIndex use the setConstraint method of it's superclass Pane, which looks like this:
static void setConstraint(Node node, Object key, Object value) {
if (value == null) {
node.getProperties().remove(key);
} else {
node.getProperties().put(key, value);
}
if (node.getParent() != null) {
node.getParent().requestLayout();
}
}
So the information gets stored directly in the node.