O.K. If you look VERY closely at the offending item, you will note that the "base" of the nipple is sandwiched between two super-thin sheets of clear plastic which serve to trap the base of the nipple., the upper sheet having a "kitten's head" profile cut out of it through which the nipple protrudes. The trick is to separate the two sheets VERY carefully and feed the nipple through. Really tricky and fiddly but it can be done. Good luck.