Need help: totaling credit card receipts

How do you finalize credit card receipts in your restaurants?  We are supposed to go by what the guest writes as a total, whether they calculate the tip right or not, correct?

Let me try to explain:

Sometimes people add the tip to the bill incorrectly, and whether or not it is benefiting the server or not, we MUST go by what the total is that they wrote in, because that is the amount that they are expecting to pay, right?

My managers are saying NO, that we total whatever the bill + tip is, and even if it is different than the total they wrote in on the TOTAL line, we have to change that amount.  I feel that is altering the bill, and it is wrong.  Does anyone understand what I am trying to say?  I don't feel like I am explaining it well...  I want to find something online about how to total, and finalize, a credit card receipt.  Can anyone help me out?
Thanks!!!