Evidently the Duke's main purpose in inviting the Count's representative upstairs to a private chamber was to discuss the matter of the dowry. This was probably the first subject they talked about, but they were just feelinig each other out. The other man probably asked the Duke what amount of dowry he was expecting and was told that the precise sum would be specified later but was expected to be in keeping with the great honor being bestowed on the girl by such a distinguished husband. The Duke invites his subordinate guest to rise:

Will 't please you rise? We'll meet

The company below then.

The Duke repeats what he had previously said about the dowry offer made to the Count:

I repeat,

The Count your master's known munificence

Is ample warrant that no just pretence

Of mine for dowry will be disallowed...

The Duke apparently asked for a specific amount of money. Perhaps he thinks it best not to show any hurry about getting his hands on the gold. He may have an unusually large sum in mind, which will be settled before all the other details of the forthcoming wedding have been arranged.

It seems at least possible that the wedding will never come off but the Count's representative never reacts but may intend to warn his master against letting his daughter marry this monster under any circumstances. Daughters were disposed of by their fathers without much concern about the girls' own feelings, but any father would be interested in making a permanent family alliance and not give his daughter away to some Bluebeard who might quickly dispose of the bride and keep the dowry.

The Duke detains the subordinate man by calling attention to the bronze statue of Neptune without realizing what a terrible impression he has made.

The word "repeat" is also a slight foreshadowing of what may become of his new duchess to be if she makes the same mistakes as his last duchess.  It serves as a warning to the Count that his daughter should be mindful and submissive, or she may share the same fate as the last duchess.

You need to include the rest of the idea-- "I repeat, 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 avowed at starting, is my object."

The Duke has basically told the messenger that he knows the Count is generous and that the dowry will be granted as requested...there are no false claims to be made on the Count's reputation and status. So therefore, the Duke expects the dowry will not be rejected since the Count will be sure it is worthily asked.  He qualifies this talk of a dowry by repeating that the daughter's hand in marriage is his primary objective, but we hesitate in believing him.