For anyone to get into the White House these days, you have to be on a list. To get on the list you have to have someone who works on the inside of the White House complex clear you in with your social security number and date of birth. The secret service then runs a background check on you, puts you on the list, and you go through a heavy security process to even access the White House compound.
What obviously happened here was someone from inside the White House (friend? client? ambassador?) cleared them onto the list, and they snuck into the party probably pretending to have lost their invitations.
But their names were not on the list.