The first $50$ even positive integers are $2, 4, 6, \ldots, 96, 98, 100$, and their sum is $50 \times \frac{1}{2}(2 + 100) = 50 \times 51 = 2550$. To reduce the sum to $2016$ we must subtract $534$. The average of the numbers removed must be less than $100$, so we need to remove at least six. To use as few numbers as possible, we first remove the five largest numbers from $100$ down. Now $100 + 98 + 96 + 94 + 92 = 480$, which is nearly there, so to bring the total subtracted to $534$ we finally need to remove $54$.

[There are, of course, many other combinations of five integers with a sum of $534$ that can be removed. ]