What I think happened is that she used what she thought was a black pen, but there were enough pigment differences that it showed up only under the strong glare of the TV cameras.
Although, Allred might have suspected something. She only handed out black & white copies of the poem and signature.
That original photo came from a screen grab from the video that CNN posted. They later noticed the different colors and edited the photo to make the ink look the same.
Black pens were two dollars each, and blue pens were only one dollar each, so Gloria Allred decided to save a dollar and buy a blue pen.