What is the reason for feeling tenderness in the knee during acupuncture?

That point is probably Liver 8. The location, according to acupuncture.com.au is “When the knee is flexed, the point is above the medial end of the transverse popliteal crease, posterior to the medial condyle of the tibia, on the anterior border of the insertion of semimembranosus and semitendinosus muscles.”

Point tenderness in the body can be interpreted as a block in the channel (in this case liver channel), and it can be due to a problem in the related zang fu organ (liver), or one of the processes/mental emotions associated with the liver (anger), it could also be because of inflammation elsewhere along the meridian (any other aches in the body? see if it matches the liver pathway), or, even more surprisingly, it could mean pain in the opposite elbow (I kid thee not). Depending on the cause of the disease, the acupuncturist will either needle points near the tender point, the tender point itself, or a point totally away from it (like the elbow, maybe)