If I say "Tea is served between 3 and 6," does it mean that tea is not available after 6:00? If I want to say that tea is still available a little past six, would it be unnatural to say "Tea is served between 3 and 7"?
'Between 3 and 6' does mean the tea service stops at 6.00. If you are willing to serve tea till 6.30, you should say that tea will be served between 3.00 and 6.30. By 'tea' do you mean just the beverage or do you mean a meal?
This is not in the meaning of 'between', but usually the only good reason for saying 'between 3 and 6' is to imply that it's not true before 3 or after 6. If the times were different, the only natural thing is to say the correct times. 'We serve tea between 3 and 6. In fact we serve it all day' sounds like a joke.