Your problem is very common and the solution is simpler than you think: use a separate phone number for ads.
Make the number in the ads different from the regular number on your site. Every call to that number is from the ad. After a month you'll have exact figures, no more guessing.
Second step: ask the agency for call and form counts, not clicks. Clicks are an intermediate metric, not your business metric. If the first line of the report doesn't say "X calls came in," the report is incomplete.
Measurement method: use a separate number with the same budget for three months, record monthly call counts. In the fourth month, pause ads for two weeks and see the difference.