As used in your example, tea is like a meal (such as lunch or dinner) where you only have tea and whatever goes with it.
So the form is the same as lunch. You would not say the lunch, if used in place of tea, in your example.
I don't believe it is an idiom.

It's no different than saying:

My aunt is coming to dinner tomorrow.

Buy any beef or chicken meal - get a Free kid's meal *

Then you put any restrictions in really small type right at the bottom of the page...

_{* Kid's meal is chicken nuggets & chips. One kid's meal offer per adult. Child must be accompanied by parent or guardian. Under 14s only. Terms & conditions apply. Participating outlets only.}

;-)

More seriously, the way you have it worded at present makes it sound like any child can walk in, buy themselves a kid's meal, then get a free large meal for their parent... which I imagine is not how the offer works.

If it's an advert - a poster or in-store offer - you need to get the essential message across really quickly. Details come later.
Get them to understand that what you are actually selling is the beef meal & the chicken meal.
The "special offer" is the kid's meal.
Don't give them the impression, however fleeting, that what they are about to pay for is the kid's meal. It's not worth the arguments at the till between your staff & the customers who don't read so well, or don't read thoroughly.