With Mr Bannon gone, the New Zealand dollar traded above US73c from US72.95 at the end of last week.
The Australian dollar was sharply higher against its US counterpart and was again firmly above US79c.
The White House confirmed on Friday Mr Bannon was leaving the Administration, prompting debate among traders whether Mr Trump could be encouraged to push policies he campaigned on and said would aid the US economy, such as tax cuts.
Craigs Investment Partners broker Chris Timms said tension had been mounting between Mr Bannon and other chief advisers, including chief economic adviser Gary Cohn, who was widely tipped to take over as Federal Reserve chairman next year, from Janet Yellen.
``The departure of Bannon might ease some of the dysfunction within the Trump Administration and the news was generally taken positively by markets,'' Mr Timms said.
In terms of global economic events, the focus this week would be the Kansas City Fed's Jackson Hole conference, starting
on Friday and running until Sunday, he said.
The key speeches from Dr Yellen and European Central Bank president Mario Draghi would take place after the New Zealand markets had closed for the week.
The conference topic this year was ``Fostering a Dynamic Global Economy''.
Dr Yellen would speak late on Friday on financial stability, in what could be her last appearance at Jackson Hole as chairwoman, as her term expired in February next year, he said.
Mr Draghi would speak on Saturday, NZ time.
Attention would focus on any potential policy hints from the Fed or ECB, although media reports suggested Mr Draghi, at least, would not signal any policy changes before the ECB policy meeting on September 7, Mr Timms said.
It would be a quiet week on the local economic front but there was no shortage of earnings reports due from both New Zealand and Australia.
This week represented the peak of the reporting season.
Some of the local heavyweights set to report included Mercury, The a2 Milk Company, Auckland Airport, Meridian Energy, Trade Me and Port of Tauranga.
Fisher & Paykel Healthcare and Infratil would hold annual meetings and there was likely to be commentary around trading conditions, he said.
In Australia, the market would hear from the likes of Amcor, BHP Billiton, Sydney Airport, APA Group, Woolworths and Medibank.
So far, it had been a solid set of results from New Zealand and Australia had been on the disappointing side.
``Results across the Tasman have generally been all right in most respects, although we have seen some high volatility in both directions from companies that have reported.
``We expect this to continue, given the calendar looks particularly heavy this coming week,'' Mr Timms said.
