I ran into some display issues with the anchors that connect Column Bubbles to a Column Grid, and discovered that there are two different object types that can be involved, depending upon how the labels were generated. It took me a while to sort all of that out, so I thought I would document it here for my own future reference as well as to share it with others.
If you create the labels by selecting a Column Grid and use the ColumnGridLabel command, or a Custom Column Grid and use the CustomColumnGridLabelAdd command, the anchor objects will be Anchor Bubble to Column Grid objects. If you use the Column Bubble tool (such as the one on the out-of-the-box Annotation tool palette), the anchor objects will be Anchor Lead Entity to Node objects.
If you use a mix of these, any display changes will have to be applied to both object types to have them display the same way.