Once a Grey Warden, always a Grey Warden. It is a military order. Hell, Duncan killed Jordy for refusing to take the Joining because the moment you agree to join, you are part of the order. Essentially Jordy drew a weapon on his commanding officer. Otherwise Duncan was guilty of murder because Jordy was only defending himself from being forced to do something potentially lethal.
However, this attitude then presented a problem with regard to various people; namely Fiona, Alistair and Anders.
Fiona apparently left the Grey Wardens because 1) the other Wardens were being nasty to her for having been cured 2) because she wanted to go back and join the Circles and cause trouble. Both these reasons sound ridiculous because you'd think it would be in the Warden's interests to study Fiona because of the possibility of finding ways to overcome the Taint and actually cure the Blight and the Wardens are allowed to recruit from the Circles specifically on the understanding they will keep the mages under control. I've always felt it looked as though the Grey Warden leadership had actively wanted chaos in the Circles and wondered even before DAI if Corypheus has in some way infiltrated their ranks. However, it would seem that Fiona leaving their ranks pre-dated his release. Presumably they approached the Circle hierarchy and asked them to take her back and Fiona was willing to agree to this because of the reasons given above.
Alistair, at least as King, you can understand because the Grey Wardens would see it in their interests to play along with the whole thing. In DAA they end up working with the monarchy and being given temporal power by them (a fact totally ignored in DAI). This can be either monarch but Alistair was a relative of a powerful noble in Eamon, so I imagine that going easy on Alistair even if not king was working in their interests. Besides by DA2 he is a hopeless drunk so the Wardens probably accepted that he was no longer fit for duty anyway.
Anders never made sense to me. Initially he managed to escape their notice but if you contact the Wardens in the Deep Roads, they seem really chilled to find him alive and no suggestion that he is actually a deserter. So again, were the leadership actually in favour of what he was doing in Kirkwall? If you don't meet them then, you can do so when searching for Nathaniel. Again, whilst Nate is initially surprised to see him because he thought he was dead, you'd think he would then report back to HQ. May be Nate was putting friendship first and kept quiet about finding Anders. Still, as Anders admits himself, he might have withdrawn himself for contact with his superiors and not "be attending the parties" but he is still a Grey Warden by virtue of his taint if nothing else. May be the leadership were turning a blind eye because there wasn't a Blight on at the time and initially Anders wasn't doing anything to cause trouble with the secular powers. However, when Anders, the Grey Warden deserter, blew up the Chantry then they ought to have taken notice and hunted him down because it reflected very badly on their order that they had not kept tabs on him in the first place, particularly considering he was a mage, and would compound the matter if they then didn't do something about him. If fact I can see how Anders blowing up the Chantry would negate all the good work that the Warden had been doing in Amarathine to show that Grey Wardens could be trusted with secular affairs. If Teagan had pointed to that as an example that Grey Wardens and other quazi-military organisations like them can't be trusted instead of harping back to Sophie Drydan, I would have understood it.
It is things like this that irritate me about the writers. They establish certain organisations, give them a plausible set of rules they operate by, and then totally ignore this when it suits their plot development.