Good morning Leigh,
When the activity setting "time limit in minutes" is not defined, Buzz will display to the student a clock button at the bottom left hand side of the activity after the exam has been started. When the clock button is selected, it expands to show a counter that counts up indicating the amount of time the student is spending viewing the exam. In that scenario, the clock doesn't indicate that the exam will end, and the time accumulated in the counter is not reviewable by other users (it is purely for the student to interpret for their own performance).
That said, there is not currently a way to remove the counter button that is displayed within exams. However, we will take this scenario into consideration for possible future updates to Buzz. Thank you for bringing this to our attention!