Does the mortage company have the right to come after me for late payments and penalties and back interest when at the beginning they refused 3 of them
I'm sorry, but your question is a little unclear. Are the saying the late payment and penalities are solely for the three payments they refused to accept while they were trying to foreclose on you eight years ago? After the mortgage company dismissed the foreclosure action, did they accept the three payments reasonably around the same time? Do you have any documentation showing that you attempted to make timely payments, but they refused
If so, consult with a lawyer to have him or her send your mortgage company a letter with your supporting documentation showing that you are not liable for late payment penalities for payments they initially refused to accept when made timely. And hopefully, your lawyer can resolve the situation to your staisifaction without there being litigation.
If the mortgage company's case against you was dismissed "with prejudice" (meaning, they lost), then they do NOT have the right to come after you unless you signed a new note since then. However, you will want to make sure you are using the correct language. Because if the foreclosure was dismissed "Without prejudice", then they can come after you again.
The fact that they refused payments is likely irrelevant. If the case was dismissed with prejudice, you would not have to pay anything.
Nevertheless, in order to give you an more accurate answer, there needs to be some more facts.