Here are screenshots of the email, followed by the similar Home Improvement offer seen as activated on my offers page
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Below - screenshot of the Home Improvement offer seen on my offers page:


If I take the approach that they are separate offers and the email is an offer for ALL purchases, I guess the question becomes what people's experiences have been if the expected credit hasn't posted after 2 billing cycles. Who does one talk to? If I say "this offer email said nothing about Home Improvement" can I expect an outcome in my favor if I've met the terms?