If a customer calls in and states that an unauthorized transaction hits their account (they stopped service but the company charged them ) is that a Reg E claim? Bank wants to deny based on the fact that it's a merchant dispute.

I would probably ask the customer to first try to resolve with the merchant, but if they paid via ACH or with a card, I don't see how it ISN'T Reg E.
This sounds like the start of 90% of the Reg E claims that I see...

Bank wants to deny based on the fact that it's a merchant dispute.

What does this statement mean????

They were told by someone that if it's a merchant dispute (don't like the color, they originally authorized pays to dr their account) not to open a reg E claim because it was not unauthorized.

If they don't like the color, I can see that possibly being a merchant dispute. But if they withdrew authorization for the debits and the company still pulls the funds, that is Reg E. R07 would be the return code, Authorization Revoked. Just because they gave authorization at one point in time does not mean the merchant then has full access to withdraw whenever.

The fact that the OP used the term "merchant dispute" leads me to conclude that the charge was posted to a debit card. Cancelling a service such as a health club membership or insurance premium may be considered a merchant dispute under VISA/MC rules, but it still meets the definition of an unauthorized/incorrect EFT under Reg E 1005.11. You are required to investigate.

You may ask the customer to contact the merchant, but remember that your provisional credit and investigation timeframe clocks are still ticking while you wait to hear back from the customer. Also, you cannot deny the claim solely on the basis of the customer refusing to go to the merchant first.

Are we required to provide the provisional credit within 5 business days or is it required when we file the chargeback? Is there a required timeframe to file the chargeback?

If you are a VISA issuer, this dispute type does not meet the definition of a fraudulent transaction requiring provisional credit in 5 day. However it is a transaction covered by Reg E requiring provisional credit in 10 days. VISA/MC rules give an issuer 120 days after the transaction date to file a chargeback for this dispute type.

Wouldn't this fall under Canceled Recurring transaction and as such the credit is not required until the chargeback is submitted similar to services not provided,defective merchandise, etc?

Are you aware of a matrix or list of dispute reasons with the applicable provisional credit requirements that I can provide to Bank personnel?