To reiterate: Mauritius claims the territory due to international law that prohibits the breakup of territories before independence. The claim is that the British have no long term rights to this territory. An agreement can not be reached. Mauritius claims that it is being harmed. The issue is referred to an international court where it will be arbitrated.  The only valid counter argument is that the breakup was legal. 

Obviously it is political and motivated by strategic interest. It is a strategic asset.   

As to African support it is entirely likely that the experience of many arbitrary and damaging demarcations during the colonial territory rush is the overwhelming factor. The USA and the UK are highly valued trade partners for most African states not to mention aid, tourism, ect ect, and more often than not there is no agenda against them.