Pardon me?

I feel a lot less sheepish when I flub up my words when speaking to an ESL student. Cause, like, they might think I'm just saying a word they don't know yet, right?

Yeah.
So when they say "Have a last day" (wha? lice? I know it was "nice" but it did not sound at all like that), it is best to smile and say, "Goo duh..." which is a combination of saying, "you, too!" and, "good!". Because, really, who doesn't respond to someone telling you to have a nice day by saying, "good".
At this point it is best if you lower your head in shame and shove your left-hand index finger underneath your top lip, but wait until the student has walked away, lost in thought over the possible definition of the new English word they just heard.