Elizabeth did get in a good zinger when Burke said he could buy Collinwood: You'd do better in invest your money in learning the rudiments of common courtesy!
I love Elizaeth's self-possession as she entertains the man who could very well destroy everything she cares about. But until that happens, she is still the Mistress of Collinwood and courteously offers her guest tea. This may be the first time Burke has actually spoken with Elizabeth. To make conversation, she asks him about his travels, and he is disconcerted by her calm assurance. (Neither of them is disconcerted that an overhead mike can be seen to the left and casts a large shadow on the wall at the right, or that she calls him “Roger” at one point.) Elizabeth is so much the Mistress of Collinwood that the fact that she herself has to make the tea only enhances the effect of her innate poise and self-confidence.
And by the time Vicki arrives and asks Burke what he's doing at Collinwood, he's so completely disarmed that all he can say is, I'm not exactly sure--I think I'm having tea.
It's a measure of his homeless, wandering life that by the end of the episode he tells Elizabeth, I've never felt so at home as I do here at Collinwood.
It doesn't help that he's falling for Vicki either.