When using connectors between shapes it can be hard to read connector text labels. If it was possible to specify the background color of the text for the connector it would be more useful and prevent “overstriked” text. This does not seem possible in Libre Office 4.3?
It is currently not possible to set a background colour for text labels of drawn shapes, lines, or connectors. The related enhancement request is fdo#50961.
While it’s not possible to set a background color, you can set a highlight color in menu Format - Character - Highlighting to achieve a similar effect.