It's an add-on that signifies an absolute necessity or need to do something or obtain something. It doesn't just mean to get something back or in return, it also can be used with just about any verb. "I have got to pass my math test." "I got to eat. I got to drink. I got to dance. etc. It's more a slang term, so in professional or formal situations i would refrain from using it. Also answering you're question as to why it's written in a past-tense form, it doesn't have a reason really, it's kind of an exception to the rules as are many things in the English language.