Hi George,
Thank you for contacting Syncfusion Support
We have prepared a sample according to the provided scenario. On analyzing the Border within the TabPanelAdv in the provided screenshot, we have found that the visualstyle for your application is "Office2013". In this sample, we have changed the reported border background using the TabPanelStyle in the DocumentTabControlStyle of the DockingManager. Similarly you can change the Background and BorderBrush for the TabPanel according to your need. Please have a look at our sample from the following location:
Sample:
DockingNew_119830Kindly try our sample and let us know whether this solution is helpful.
Regards,
Vijayalakshmi V.R.