Spots that never come off

"'Course Dumbledore trusts you,' growled Moody. 'He's a trusting man, isn't he? Believes in second chances. But me – I say there are spots that don't come off, Snape. Spots that never come off, d'you know what I mean'" Severus Snape is a little shaken after his unfortunate encounter with Moody Mad-Eye. Should he go see the Headmaster?