"Manage Connections" is the title language string _UE_MANAGECONNECTIONS. You can remove it by setting it empty within your CB language files. "No Pending Actions" is displayed if you've no pending connection requests and is the language string _UE_NOACTIONREQUIRED. You can also remove it by setting it empty within your CB language files. You can find your CB language files at the below location. Please see your CB documentation available for download in the Advanced downloads section for further language usage information.
components/com_comprofiler/plugin/language/
You can also use CSS to hide them if you like. The below should work.
Code:
.cbManageConnections > .contentheading,
#cbtabaction > .tab_Description {
display: none;
}