Det Supt Suzanne Chow said McGill was confused when officers finally turned up at his door on 4 December 2019.
She said: "He was quite tight lipped. You could tell he was shell-shocked and he probably wasn't expecting his past to come back and haunt him 35 years later."
Following his conviction last month, the jury was told he had also sentenced to life in 1999 for a brutal assault with intent to ravish and released on licence in 2007.
The 59-year-old was jailed for life yesterday, Tuesday, and ordered to serve a minimum of 14 years in prison.
Judge Lord Burns said McGill had murdered Mary after a "chance encounter", and that he had shown no remorse.
"Hopefully he dies in jail," said Mary's son Martin after the sentence.
Officers now hope the prosecution will now give hope to other families waiting for justice.
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"These cases are not forgotten about," Det Supt Chow said. "Just because they are not resolved at the time doesn't mean that we don't still think about these people who have been victims of crimes and that we don't think about their families."
She added that McGill's conviction also sends out a powerful message to other cold case killers.
"Your past doesn't go away. It will come back and haunt you one day."