What is "but they do it'?
Someone invaded someone else's hometown and took the mayor's mansion as their headquaters. And the invaders asked two servants to help them move a table. The servants were complaining as below:

"What right coming in at all?" said Joseph.
"None," sand Annie.
"None," repeated Joseph. "I see it like they have no right at all, but they do it, with ther guns and their parachutes; they do it, Annie."
"They got no right," said Annie. "What do they want with a table in here, anyway? This isn't a dining-room."

Question

What is "but they do it'?
Someone invaded someone else's hometown and took the mayor's mansion as their headquaters. And the invaders asked two servants to help them move a table. The servants were complaining as below:

"What right coming in at all?" said Joseph.
"None," sand Annie.
"None," repeated Joseph. "I see it like they have no right at all, but they do it, with ther guns and their parachutes; they do it, Annie."
"They got no right," said Annie. "What do they want with a table in here, anyway? This isn't a dining-room."

Answer

Gary already answered your question. I'll just add to it a bit more...

...but they do it regardless.
...but they still do it.

"It" here refers to them forcing their way in. How did they do it? With their "guns and their parachutes" apparently.

Answer

You could interpret it as 'but they do it anyway' or 'but they do do it'.
i.e. they do it, despite not having a right.
The writer wrote their dialogue in a clipped dialect, which is probably why they dropped a word.

Answer

They didn’t have any right at all to invade us but they did it anyway.
Like I see it, they had no right at all, but they did it anyway.