How we cite our quotes:
'I [Clennam] want to ask you, mother, whether it ever occurred to you to suspect—[...]--that he had any secret remembrance which caused him trouble of mind--remorse? Whether you ever observed anything in his conduct suggesting that; or ever spoke to him upon it, or ever heard him hint at such a thing? [...] Is it possible, mother,' her son leaned forward to be the nearer to her while he whispered it, and laid his hand nervously upon her desk, 'is it possible, mother, that he had unhappily wronged any one, and made no reparation? [...] For Heaven's sake, let us examine sacredly whether there is any wrong entrusted to us to set right. No one can help towards it, mother, but you. [...] In grasping at money and in driving hard bargains--I have begun, and I must speak of such things now, mother--some one may have been grievously deceived, injured, ruined. You were the moving power of all this machinery before my birth; your stronger spirit has been infused into all my father's dealings for more than two score years. You can set these doubts at rest, I think, if you will really help me to discover the truth. Will you, mother? [...]If reparation can be made to any one, if restitution can be made to anyone, let us know it. (1.5.38-49)
Arthur has grown up in a house filled with secrets and lies, and he is haunted by the vague feeling that he needs to recompense someone for something. Why doesn't Mrs. Clennam think this is her duty too? How do their conceptions of duty differ?
'Amy, Mr. Clennam. What do you think of her?'
'I am much impressed, Mr. Dorrit, by all that I have seen of her and thought of her.'
'My brother would have been quite lost without Amy,' he returned. 'We should all have been lost without Amy. She is a very good girl, Amy. She does her duty.'
Arthur fancied that he heard in these praises a certain tone of custom, which he had heard from the father last night with an inward protest and feeling of antagonism. It was not that they stinted her praises, or were insensible to what she did for them; but that they were lazily habituated to her, as they were to all the rest of their condition. He fancied that although they had before them, every day, the means of comparison between her and one another and themselves, they regarded her as being in her necessary place; as holding a position towards them all which belonged to her, like her name or her age. He fancied that they viewed her, not as having risen away from the prison atmosphere, but as appertaining to it; as being vaguely what they had a right to expect, and nothing more. (1.9.23-26)
Dorrit twists the idea of duty to fit his own selfish purposes. Basically, whenever he likes something Amy does, she's being dutiful, and whenever she does something he disapproves of, she's being undutiful.
"[…] you'll memorialise that Department (according to regular forms which you'll find out) for leave to memorialise this Department. If you get it (which you may after a time), that memorial must be entered in that Department, sent to be registered in this Department, sent back to be signed by that Department, sent back to be countersigned by this Department, and then it will begin to be regularly before that Department. You'll find out when the business passes through each of these stages by asking at both Departments till they tell you. [...] When the business is regularly before that Department, whatever it is,' pursued this bright young Barnacle, 'then you can watch it from time to time through that Department. When it comes regularly before this Department, then you must watch it from time to time through this Department. We shall have to refer it right and left; and when we refer it anywhere, then you'll have to look it up. When it comes back to us at any time, then you had better look US up. When it sticks anywhere, you'll have to try to give it a jog. When you write to another Department about it, and then to this Department about it, and don't hear anything satisfactory about it, why then you had better--keep on writing. [...] Try the thing, and see how you like it. It will be in your power to give it up at any time, if you don't like it. You had better take a lot of forms away with you. Give him a lot of forms!' With which instruction to number two, this sparkling young Barnacle took a fresh handful of papers from numbers one and three, and carried them into the sanctuary to offer to the presiding Idol of the Circumlocution Office. (1.10.91-106)
Besides being a hilariously honest description of the rigmarole Arthur would have to deal with if he really wanted to take up the task of figuring out the Dorrit case, this passage has a pretty telling detail. It would be Arthur's responsibility to follow the case from department to department, because no one would notify him about it. Basically, the Circumlocution Office farms out its labor to people who don't work there.