Major credit card company is not accruing the correct cash back percentage that was agreed to per card benefit - should be 4% but accruing only 1%

I have a credit card issued by large, global bank/credit card company (based in US - $70 Bil in revenue) that has an exclusive partnership with a major national US retailer ($120 Bil in revenue, 85 mil US members). The credit card offers 'cash back' program which is the major benefit of this card. The cash back percentage on a purchase varies from 4% to 1% depending on the category of the type of products and services purchased on this card. I was concerned that a certain regular purchase I made was not accruing the 4% cash back the benefit promised. So I manually calculated the cash back amount I should have gotten for all the purchases made in the particular category over a 6 month period and my analysis concluded that I was being shorted compared to what I was actually credited. Do I have a case and if so, what type/kind of lawyer do I need? Thanks