Roughly… If your string is flat and you are tuning it up you are making the string tighter, but with pedal engaged the forks are grasping the string and it doesn’t slide past perfectly so some of the tightness is caught above the fork.
It’s also possible the harp just needs to be regulated. If there is some overmotion then when you put the pedal into flat and then back into natural the natural disc may not be in exactly the same position as it was the first time. But only a technician working on it can tell you exactly what is going on.
Also, you didn’t mention which string you were tuning that this was happening to. If the string is old, there could be a little dip or gouge in the string where the pins of the disc grab it. If you move the pedal to flat and then back to natural, maybe the disc is not grabbing the string in exactly the same place(in the gouge area) causing the pitch to be higher.
There is a little trick that can help you with this. When you tune the string (set to flat), be sure to press the upper part of the string (around the tuning discs) with your fingers inwards when you are done. This will make the tension of the string equal throughout the whole length of the string, not only in the lower part (from the discs to the soundboard). Hope I was clear. 🙂