Johnny, 

The ‘le’ is hardly perceptible in everyday spoken pronunciation of ‘ moins le quart ‘. I think this might be noticed more readily here because overall the rate of speech in the dictation is otherwise relatively sedate and comprehensible compared to that of many native speakers !

At C1 level,  there will/should be many ‘ swallowed vowels’ and informal elisions/glidings to ( not ) hear, as it is near-native speaker standard, by definition.

See the note on pronunciation of ‘ moins le quart ‘ in attached link :

 https://www.frenchtoday.com/blog/french-vocabulary/how-to-tell-the-time-in-french/