As the title said, bank account should have not been counted for activity check.
I don't know much about what programming language are used to create the toriclan and activity check, but i have the basic idea on how to handle this.

Whenever you create a rank, there will be a checkbox for what that rank could do (sent wars invite, invite member, etc). By adding a new checkbox to indicate that rank is for clan bank, you could limited that rank could only hold one account (to avoid people circumventing the activity check) and be recognized as the clan bank.

As for the activity check, whenever they do the check on the toriclan and calculating the point. When they met the condition where there is a rank that hold a unique key as "clan bank" they should skip it.

tl;dr

• Add new checkboxes in clan rank management for "clan bank".
• Assign "clan bank" as a unique key.
• Make a rank that has the unique key of "clan bank" can only hold one account.
• On the activity check, if they met the unique key of "clan bank" they skip it.

Discuss and some new idea are appreciated. Hope, site dev notice this thread.