You have to wonder, really, if they had the "right" since they gave up their titles in 1917.
I don't know if they just stopped using them and adopted other titles or they had to renounce them officially(to the ones who bestowed them) in order to adopt others...there is the story that Patricia and Pamela,while visiting Germany,signed themselves as "Prinzessin von Battenberg" long after 1917,of course!
On the other hand,some other family members had right until the end of their lives to be just Prince/Princess von Battenberg,like Princess Anna until she died...
There would be an interesting situation if the whole Battenberg/Mountbatten family would meet after 1917,for example,in Sweden,(still a monarchy who still recognize titles)...Who would take precedence?
Lord or Lady Mountbatten over Prince Francis Josef von Battenberg due to seniority in the family or maybe Prince Francis Josef to to the fact that he was still Serene Highness and the other members are not?