Is the Brooksdale Email or Letter a Scam?

I received the Brooksdale letter below telling me I had overpaid income tax for the year April 2021 to April 2022. The letter claims I will be sent a cheque to Brooksdale LTD within 14 days. I was skeptical about the email so I contacted HM Revenue and Customs by email, though the letter told me I didn’t need to do so. I got a reply that the Brooksdale email is a scam. It seems Brooksdale is trying to get bank details to "put the money into it' after they’ve taken their share. The letter's poor-quality paper made me wary and I was right. Please be careful!