First of all Welcome to Pet Talk & enjoy all the talks & pictures..
Now for your question = I would suggest putting patchs or stripes of double sided tape on the outside of screen door.. (you need double sided for one side to stick to door & other side for the cats paw to sticky too // can find at Walmart or hardware store).. Cats do not like sticky on paws.. See the kicker is Do Not Use anything that can danger your baby.. The double sided tape is very safe & then after a while your baby will catch on & stop doing this.. Also you can use very small amount of liquid smoke to rub thin layer on the tape due to they do not like the smell.. Again I Stress Make Sure Your Baby Is Not Harmed.. Good Luck

helene