Hackers held Travelex to ransom, demanding the firm pay $6m (£4.6m) before they unlock its systems.
That has affected banks like Barclays, Lloyds and RBS, which use Travelex to provide their travel money services.
And Travelex has refused to say when some services will be restored.
In a statement, the foreign exchange firm said it is making “good progress” recovering its systems.
The firm is hoping that employees in its stores, who have resorted to using pen and paper since the hack, will be able to switch on their computers again by the end of this week.
But its website, which was taken down immediately after the attack was launched two weeks ago, is still offline.
Travelex has not said when it will be back up and running.