Is there an idiom or saying for an act that on the surface appears extending the olive branch but in reality it means to abscond responsibility
Solution 1:
What you want is something along the lines of "Let's agree to forgive ourselves my trespasses"—but I don't know of any idiom in English that expresses that particular sense of mutual magnanimity toward one party's misbehavior. The closest one may be let bygone be bygones, which Christine Ammer, The American Heritage Dictionary of Idioms, second edition (2012) defines as follows:
let bygones be bygones What's done is done; don't worry about the past, especially past errors or grievances. For example, Bill and Tom shook hands and agreed to let bygones be bygones. {First half of 1600s}
Although this expression is neutral as to where fault lay in the original source of conflict, it doesn't require that both parties have been at least somewhat at fault. Still there is an implication that the grievances were not all on one side. More strongly suggestive of fault on both sides is forgive and forget (often anachronistically expressed as "forget and forgive"), which Ammer defines as follows:
forgive and forget Both pardon and hold no resentment concerning a past event. For example, After Meg and Mary decided to forgive and forget their differences, they became good friends. This phrase dates from the 1300s and was a proverb by the mid-1500s.
In effect, the offending person in your scenario is telling the offended person, "Get over it." Here is Ammer's entry for that idiom:
get over ... 2. Recover from, as in I just got over the flu, or I hope the children get over their parents' divorce quickly. {c. 1700} This usage sometimes appears as get over it, as on a bumper sticker following the 1992 presidential election: "Bush Lost, Get Over It."
The flippancy of the bumper sticker example is perhaps even more annoyingly evident in a situation where a person at fault seems impatient for a return to the status quo ante, as though forgiveness were a right claimable under some sort of ethical statute of limitations.
Solution 2:
Tacit agreement. It's an agreement you have but don't really talk about.
For example - a wife who knows her husband is having an affair - but chooses not to discuss it. She has a 'tacit agreement' (unspoken agreement) with her husband for the affair - and their marriage, to continue.
'Tacit' is Latin for 'silent'.
https://www.google.com.sg/search?q=tacit+agreement+meaning&ie=UTF-8&oe=UTF-8&hl=en-sg&client=safari
Tacit agreement may exist entirely without words or there may be some agreement or disagreement followed by the 'tacit agreement' - which may be, just to go on, as if nothing has happened.
To 'agree to agree' - rather than genuinely agreeing.
Solution 3:
A non-apology.
Below taken from Wikipedia:
Sarcastic examples
Humorist Bruce McCall, in a 2001 New York Times piece entitled "The Perfect Non-apology Apology", defined the term as referring to "sufficiently artful double talk" designed to enable one to "get what you want by seeming to express regret while actually accepting no blame," and suggested some tongue-in-cheek apologies, such as:
Nobody is sorrier than me that the police officer had to spend his valuable time writing out a parking ticket on my car. Though from my personal standpoint I know for a certainty that the meter had not yet expired, please accept my expression of deep regret at this unfortunate incident.[19]
Solution 4:
You're expressing the idea that the aim of the appeasement was to limit their own responsibility.
Consider calling this damage control (US) or damage limitation (UK).
damage control / damage limitation noun Action taken to limit the damaging effects of an accident or error. ‘I needed to talk to Stephanie right away and do some major damage control.’ - ODO
Damage control is action that is taken to make the bad results of something as small as possible, when it is impossible to avoid bad results completely. REGIONAL NOTE: in BRIT, use damage limitation - Collins
If it was simply a token measure to allow them to walk away, you can call it an excuse.
excuse noun 1 A reason or explanation given to justify a fault or offence. ‘She glared at Sean with a look that conveyed that she didn't buy his excuse for a second.’ - ODO