Answer:
The contextual meaning of the phrase "take up" in the story will mean the actual practice and use of grammar in speaking Italian.
Explanation:
To take up something basically means to try to practice, put into practice and use or do it in action anything, the thing being taken up. It is a phrasal verb that implies the start and use of anything.
<em>For example, to take up tennis means to practice and start playing tennis.</em>
Likewise, when the major said "to take up the use of grammar", he means that he should actually put into practice and start using and learning grammar.