I am so sorry this happened. If it wasn't over 30 days late you should not see any change to your credit score. I would contact someone in the credit depart of Target and ask them to remove it. You can also file a dispute with the credit bureaus.
Many many years ago I paid my $50.00 student loan late. I made the payment via mail, told you it was a while ago, then received an email that the payment was late. Thinking the payment and email just "got crossed" I ignored it. I should add that I made ONE payment, I never realized that it encompassed 13 student loans, because you take out several per semester. It dropped my score by 155 points!!!! I have begged, pleaded, disputed, anything and everything you can think of and no one will do anything! To this day it still shows I was late times 13! Luckily my score has recovered, but man!