Why does the Duke apparently try to forestall the envoy's rushing down the stairs at the end of "My Last Duchess"?
The Count's representative jumps up without warning and starts to flee down the stairs. He is horrified by the Duke's character, which is what Browning intentionally reveals throughout the poem. The Duke seems surprised that he has made a bad impression. He tries to forestall the other man's departure because nothing has been settled. He had brought the Count's representative upstairs ostensibly to show him part of his art collection, but really in order to settle the sum of the dowry the Duke would receive upon marrying the Count's daughter. That is why the Duke brings up the matter of the dowry even while the other man is fleeing.
The Count your master's known munificence
Is ample warrant that no just pretence
Of mine for dowry will be disallowed;
Though his fair daughter's self, as I allowed
At starting is my object.
The Duke then calls attention to a sculpture of Neptune taming a sea-horse, as if to try to renew the pretence that they are there to view the art collection. The Duke obviously knows nothing and cares nothing about art except for its cash value and for the prestige it gives the collector. He does not like the way it would look for the Count's representative to come rushing down the stairs by himself. The guests gathered below would get the impression that the meeting between the two men had ended in complete disagreement. The representative doesn't seem to care how it would look or how the Duke feels about his abrupt departure. It would appear that the representative intends to warn the Count his master not to let his daughter marry this monster under any circumstances, because the Duke is quite capable of having the Count's daughter murdered if she failed to live up to his impossible requirements and probably using her dowry to add another work of art to his collection. The Duke, of course, is so insensitive that he doesn't realize what a terrible impression he has made on the other man-- as well as on the reader. The Duke seems like a madman, almost like a Bluebeard. The reader is left wondering how many duchesses the Duke might have already married and then disposed of.