https://www.uscis.gov/forms/filing-guidance/form-i-797-types-and-functions
It's more about airlines and less about Mexico border control from what I understand. There's very few airline staff who can distinguish I-797 from I-797A.
When I travelled with extension letter, one airline got confused about the letter (48 months) and called the manager. The manager said: "You need to add 4 years to expiration as extension letter says." I expect this level of education, unfortunately, which makes it hard to convince I-797, I-797A and I-797C are different forms 😊