The correct answer is to ask the journal how to proceed.
Regarding the statistics, you don’t what the exact p-value is. Remember that t p-value is some kind of integral of a density. When you get out that far in the tail of a density, the numerical methods break down. Is is $10^{-16}$ or $10^{-17}$ or $10^{-14}?$ Who knows!? But it also does not matter. The number you’re getting is R’s way of telling you that the answer is basically zero.