There's a small, confused smile as he finally looks upon his brother's face; he's older, Mycroft can tell that much. Older - not by terribly much, but still older - and judging by the shawl and mussed up hair, a wee bit under the weather. "A proper cup of tea would be a godsend," Mycroft knows to tell Sherlock as he slips inside.
He's not yet the stern and proper man Watson knows him as, so he just stands there for a few seconds, hands in the pockets of his coat, unsure what to do. He could sit down on the sofa, but Sherlock's obviously feeling a touch more delicate than he is right and so he fights his urges for a moment and then slips past him.
He'll take care of the tea.
Of course that means that he has to look through cabinets to find the tea leaves, the pot and cups. But that's a small inconvenience.