I believe Kim's sister saw that Kim was given a marker style pen like Trump.
Kim's sister swapped out the 'marker' for a brush pen (see pics related)
She likely did it so that Kim would be more comfortable in writing his signature.
Notice it's brush strokey, like you would see in Asian calligraphy?
The marker was then swapped back in after signing, so as to return it to it's owner.
Very respectable.