Are you required to make another bracha on your tefillin if you take them off to check the parshios?
With tefilin, if you had in mind when putting them on that you might be taking them off and later putting them back on; then as long as you weren't in a situation in the middle that you COULDN'T have worn tefilin, the original bracha covers it.
So bathroom breaks require a new bracha. If you took them off for five minutes to help carry suitcases, you wouldn't need a new bracha.
Certainly wherever you're checking your tefilin is a place where tefilin can be worn; but I wonder if there's enough of a pause and concentration needed to open and check tefilin if you can still have that in mind. But in theory yes.