Tyrion tells us in his own response to Robb...
It means he is not welcome and as a sign disrespect.
"Any man of the Night's Watch," the dwarf repeated, "but not me, do I take your meaning, boy?"
Robb even goes as far as to point the sword directly at Tyrion making the threat perfectly clear.
Robb stood and pointed at the little man with his sword. "I am the lord here while my mother and father are away, Lannister. I am not your boy."
"If you are a lord, you might learn a lord's courtesy," the little man replied, ignoring the sword point in his face. "Your bastard brother has all your father's graces, it would seem."
Tyrion in well aware of what is going on even takes a small verbal jab at Robb to which Robb jabs right back.
"Jon," Bran gasped out from Hodor's arms.
The dwarf turned to look at him. "So it is true, the boy lives. I could scarce believe it. You Starks are hard to kill."
"You Lannisters had best remember that," Robb said, lowering his sword. "Hodor, bring my brother here."
It is not until after Tyrion presents Bran with the special saddle does Robb soften.
Robb Stark finally sheathed his sword. "I … I may have been hasty with you," he said. "You've done Bran a kindness, and, well …" Robb composed himself with an effort. "The hospitality of Winterfell is yours if you wish it, Lannister."
But Tyrion has already had enough of Robb and leaves anyway.
"Spare me your false courtesies, boy. You do not love me and you do not want me here. I saw an inn outside your walls, in the winter town. I'll find a bed there, and both of us will sleep easier.
This is all confirmed directly by George R. R. Martin at an event with fans.
Another subject was guest rights. He mentioned the time the Tyrion came to Winterfell and Robb met him with bare steel across his lap. That meant that there was no guest rights for Tyrion.
So Spake Martin, ARCHON MEETING, October 5, 2001