In terms of normal everyday English, we would expect some sort of determiner before brain, be it their or the or a.
There are several ways that this sentence can be considered grammatical. The first is if the caption is seen to use 'headlinese', that is the type of English seen these days (but not always) in headlines; articles and other words such as the verb to be are omitted. Of course it would be better to be consistent and omit the their before hands also.
There is also a certain type of 'abbreviated' English (there may be a technical term to it, and it is similar but not the same as headlinese). This is the kind of English we use when we make lists or instructions, and in this case articles are omitted. So I could make a list of things to do and write
1 return book to library
2 drop off shirt at laundry
3 drive friends to movies
The articles are omitted in such a list.
Many recipes, which are instructions, leave out the the before oven in such a statement as
Preheat oven to 350°.
Then, of course, there are stereotypical but real signs such as
Beware of dog
Some people want to say that the is omitted before dog to save space. But it can't take that much more space to go ahead and include it. So this is some kind of cautionary statement. Perhaps the omission of an article is to avoid saying how many dogs are on the property, but why not just write 'Beware of Dogs'? Another interpretation is that dog could be considered as a 'unique role' here, and we can omit the article in that case ('We elected him to be president'.) For instance, someone could stick a sign up in front of the White House saying Beware of President and it would be grammatical. Here, though, dog would have to be thought of as short for something such as guard dog.
Whatever the case, the caption would be more consistent if it either used or omitted their before both brain and hands. And yes, certainly in unmarked or everyday spoken English, we would expect a determiner before brain.
It could also be an intended grammatical mistake to mean that people who write fast also make grammatical mistakes!
It is also grammatical if brain is being used as a non-count noun in the same sense as brain matter (analogous to grey matter). People are free to be creative with language and their use of words. However, we don't know the author's intention in this case.
Matter, when it means substance, is a non-count or 'uncountable' noun.