Symbols on 40244 in circuit diagram
It means....

Nothing. The symbol is entirely correct without it. The right arrow symbol denotes a function with an enhanced level of output (e.g. buffer or line driver) flowing from left to right and the down arrow symbol denotes a 3-state output. The upper rectangle denotes a control block associated with the lower rectangles, which in this case simply consists of an enable signal. There is no need to mark the inputs with anything unless they are controlled by different elements of the top block (for instance, if you combined the two separate halves of the device into one symbol) and, even then, you'd use a D not an O.

I say the symbol is correct without it, actually it isn't really. The enable line should EITHER have a circle to show it's inverted OR a bar over the name but not both.

I suspect someone entered the symbol definition incorrectly into the CAD system ages ago and people, like you, have been scratching their heads ever since. Texas used to use these sorts of symbols in their data books but I think they've dropped them now - probably because to understand them you had to pay for the relevant ANSI/IEEE/IEC standards and nobody ever did.