The phrase 'Be That as it May' means even if what you say is true.
Example of Use: "Be that as it may, I still cannot help you."
The idiom 'be that as it may' is English in origin, dating back to Geoffrey Chaucer’s time, when it appeared as 'Be as be may.' In Old English, 'mæg' meant 'am able' as the verb 'may' does today. The term was also used in Old English as an auxiliary of prediction.