The OP being delinquent once for over 120 days is an event that was reported to the credit bureaus. As a single event in time, that will stay there for a while, and will adversely impact their credit score as long as it's there.
Being 120 days late is a pretty big deal in the eyes of the credit scoring algorithm. Lenders figure that someone might be 30/60/90 days late for a variety of reasons (illness, forgetfulness, out of the country, temporarily busy with life), but 120 days starts to look bad.
OP, you can't really dispute the delinquency with the credit bureaus because it sounds like you were in fact late on your payments.
You can put an explanatory note on your credit bureau, but the credit score algorithms won't read that note and a lot of credit issuance is automatic. You can hope that if you appeal a credit decision the lender will read the note.
Your score will heal over time as you provide more data points that you're paying your bills. I don't know how long, but I'd guess it'd be several years.