Is it permissible to open a savings account at Al Baraka Bank Tunisia, whose employees claim its transactions are Islamic and supervised by a group of scholars, while others question its legitimacy?

The consideration is not whether the bank is named "Islamic," but rather its adherence to Sharia regulations in its dealings, because the judgment on a bank depends on the absence of Sharia violations. We have no specific knowledge of this particular bank, and the questioner should inquire about it from trustworthy scholars in their country.