In order to save $500,000 in this year’s budget, the city council vote

So what the argument mention is that
If the initial salary was $1000, the city council has planned to freeze it.

This decision is a foolish one and not at all supported.

The cursory inspections that will result from this action will cause many structural defects to go undetected, resulting in millions more dollars being spent on repairs in the future.

So the author clearly assumes that safety inspectors wont do their job perfectly or efficiently.

A) City inspectors are already overpaid and so the wage freeze is warranted. ​
This is not at all relevant to the scope of the argument.

B) The city council cares less about the safety of the school children than it does about saving money. ​
This is way OOS.

C) If they do not receive an increase in their wages, school inspectors will become lax in performing their jobs. ​
The same was derived by us as well.

D) The council does not feel that cursory inspections will necessarily result in defects going undetected. ​
Nothing is mentioned about this in the argument, OOS.

E) The council will not authorize repairs in the future, so it will never have to incur the extra costs
Not relevant to the scope of the argument, "future".