You can say it either way, in this context.
"We hear every damn day about how it's a shame (what a shame it is) that we can't work together to get things done."
It's fine either way here, because the speaker is simply conferring information and is not giving an exclamatory statement.
As you can see, the word order changes, because "what a shame" is a set pattern. In statements, you can use either of the phrases interchangeably. However, as you showed above, there can be some differences based on context that change the meaning.
"What a shame" is most often used as an exclamation of ones regret, disappointment or sorrow.
"What a shame they couldn't come." means that the person feels disappoint that the person they expected to come didn't.
You wouldn't really say "How it is a shame!" as an exclamatory statement, but rather as a question as you showed.
"How was it a shame that they couldn't come." means that the person does not understand why the other person's absence is regrettable.
I hope I have explained this well enough and that I am understandable. Please let me know if there is still something that is unclear.