My pewter tankard is annoyingly lacking in detail, as it simply reads 'BBC TV Quiz Ball, Challenge Match 1972'. It turns out there were actually two challenge matches that year, and I cannot find any report of who won them and who might have been presented with the souvenir. But no matter, my research did reveal the fact that Scotland won Series 7 of Quiz Ball and then took part in a challenge match against the British Lions rugby team. Later that year, Northern Ireland met a team of Olympic medallists in another challenge.
Among a few oddities: Terry Neill was a Quiz Ball stalwart who featured in the very first programme in 1966 for Arsenal and the very last one in 1972 for Northern Ireland; his team won both series. Rangers manager Scot Symon appeared in the show in 1967 but had been sacked by the time it was broadcast. Dr Who actor Jon Pertwee was roped in for Dunfermline Athletic as a last-minute substitute for Jimmy Logan in the 1971 final, and came away with a winner's medal.
There are several online articles about the series, and perhaps the most comprehensive is by Vince Cooper at The League. There is also the story of Celtic's victory in 1970 on Celtic Wiki.
Few videos of the show survive, although the very first edition in 1966 between Arsenal and Nottingham Forest is on YouTube. Recorded at Hornsea Town Hall, it is remarkable for all sorts of reasons, not least the pipe-smoking Forest team. As the show featured four 'own goals', it quickly led to a change of format so that goals were more likely to be scored by getting questions right rather than getting them wrong.
Quiz Ball was originally devised by Bill Wright, the show's producer, who was in charge of the BBC Quiz Unit and who also came up with the concept for Mastermind. That perhaps prompted another link, as Magnus Magnusson appeared twice on Quiz Ball as a guest supporter for Kilmarnock, despite later admitting that he had no connection with the team.
You can access the full results document here (pdf). A few details are missing so if you can fill in any of the gaps please contact me.