There's only one correct way to insert the S Pen back into the Galaxy Note 5 but soon after the handset was launched last year it was discovered that inserting it the other way around ended up damaging the pen detection feature of the Galaxy Note 5. It was the first time that a Note series handset featured Samsung's patented push-to-eject mechanism for retrieving the S Pen.
Samsung first came up with a simple and very obvious solution to this problem, it recommended that users follow the instructions included with the Galaxy Note 5 to ensure that they don't reinsert the S Pen the other way around. That didn't help much though so it started shipping new units of the Galaxy Note 5 with a warning label that explained the right way of inserting the S Pen.
It appears that Samsung has now taken a concrete step to ensure that users don't end up killing the pen detection feature on their phablet by inserting the S Pen the other way around. A new report points out that Samsung is producing new circuit boards that have a safer detection mechanism, the greyish white tab on the new circuit boards appears to have been designed to allow safe ejection of an S Pen inserted backwards without damaging the pen detection feature. From the looks of it, the fix involved adding an external cap piece over the original design and according to the source mentioned in the report, this little change makes a significant difference.
You're still out of luck though if you purchase the Galaxy Note 5 before this change was made, and since Samsung hasn't really made this change with much fanfare, it really can't be said for sure from when it has been shipping units with the new circuit boards. Continue to exercise caution and common sense when ejecting and inserting the S Pen in the Galaxy Note 5.