I hadn't thought about it before, but on reflection, I do too. And I wouldn't be surprised if most people do.
Exaggerated a bit for effect, it would me more or less:
There = thehr
Their = thayr
They're = thay-r
"There" is just simple and straightforward with a pure short 'e' sound and no particular stresses.
"Their" has more of a long 'a' than a short 'e' sound, and a bit of stress on the vowel sound.
"They're" also has more of a long 'a' sound and it's pronounced just a fraction longer than in "their", and there's a very slight pause between the vowel sound and the 'r'.
Huh... learn something new every day.