grep is for filtering, map is for transforming.

my @wetrasnfer_fix = map /([0-9]*_[0-9]*)/, @wetransfer;
[download]

With 5.14+, you can also use the "return" substitution modifier:

my @wetrasnfer_fix = map s/\.tif$//r, @wetransfer;
[download]

Or, you can use split:

my @wetrasnfer_fix = map +(split /\./)[0], @wetransfer;
[download]

Note from stevieb: You should also handle the case when not only the chdir fails, but the mail fails, too.