Signage for The Big Deal and 99p promotions, which were both launched earlier this year, have been taken down in stores and withdrawn from the website.
One industry insider said Aldi was returning to the European Aldi model of everyday low pricing and moving away from flagging up promotions.
"It will be interesting to see if it has moved away from this activity permanently. It is still spending a lot on national advertising, but seems to have gone back to advertising its 'when it's gone it's gone' non-food offers again."
The colour scheme of Aldi's ads has also been changed back from black to blue in the weeks since Burger has taken charge.
"The ads had changed to an M&S-style black in recent months, but have changed back to blue, which is more like the style Aldi uses on the Continent," the insider said. "This is a sign that it is trying to move away from appealing to ABC1 shoppers and go back to its discounter roots."
Previous MD for the UK and Ireland Paul Foley was replaced last month by Burger, who is on the parent company Aldi Sud's supervisory board.
Aldi's sales growth has slowed from 25% at the end of last year to 8.1% in the 12 weeks ending 10 August, according to TNS Worldpanel data.
It continues to advertise its Super6 fruit and veg promotion in store.