CCTV images captured two men taking the commodity from outside Hugo’s restaurant at 8.40 am last Friday morning.
The men were white and wearing hi-vis clothing, but no further description has been made available.
A Police Scotland sergeant explained the duo loaded four containers in to the back of a white Mercedes van before making off.
And a spokesperson for Hugo’s said: “We just can’t believe how brazen they are, especially during operating hours of business.”
Meanwhile, it is believed other premises in Moffat and Beattock have been approached or had used oil taken.
Anyone with any information or who has also been a target should contact Police Scotland on 101.