ETA - thinking on it, I don't know that I would ever expect an entire batch of cookies to be just for a three year old. That's a lot of cookies for one person. In general though, when house guests bring food of a good quantity to the house, we all usually end up eating it together so maybe that's just what I'm used to.
Exactly. If she'd brought a pan of her son's favourite lasagne with her and said "I've brought you your favourite lasagne!" no one would think he was supposed to eat the whole thing alone.
The fact the 3 year old is taking it literally could be addressed in lots of ways. I'd just tell Grandma up front that the kid is misunderstanding so let's be careful how to speak about the cookies.
Maybe it's just me, but I don't think the lasagna comparison really works.
1) Lasagna is not a typical gift item. At least in my area nobody is going to mistake lasagna for a gift because in normal circumstances it simply isn't one. Cookies, on the other hand, are an extremely common gift item, so it makes perfect sense for someone to take Grandma's phrasing as gifting to a single person.
2) Lasagna is a 'meal' item, while cookies are more a 'snack' item. Meal items are, when it comes to a household, generally expected to be shared and in fact not generally expected to be. Kind of a gray area.
A better comparison would be bringing, say, homemade beef jerky and presenting it as a gift to a particular person. The fact is, she's taking a popular gift item, presenting it to a particular person as 'for them' and then digging in like she owns it.
To use your lasagna comparison- this is like if Grandma brought a lasagna, told her son it was for him, then popped it in the oven without his or the OP's knowledge, while most of the household was gone and, when it came out, served herself and her husband each over a quarter of it, leaving them the leftovers.
Oh, and we have to assume that she's bringing a smaller lasagna in the first place, maybe the size of those frozen lasagnas, since she's only bringing a small amount.
Also, when I make cookies, I can't get 32 to last longer than three days(tops!) with three adults in the house, how long is Grandma expecting 20 to last between four adults and a toddler?
*The contents of this post are based on my limited experience: Experiences may vary with locale and culture*