Vayechi

After Yosef and the brothers came back from burying their father, the brothers were fearful that now Yosef would get back at them for all that they did to him. Therefore, they said to him that their father had requested that they should ask him for forgiveness & that he should forgive them.

Yosef wept as he assured them that since he bore no grudge, they have nothing to fear. The end of that posuk states וידבר על לבם ,and he spoke to their heart.

Rashi explains that Yosef elaborated on the reasons that they had nothing to fear. He explained: “Before you came down here, the Egyptians would make fun of me saying that I'm a slave but now that you arrived here, they realize that I really was a free man. If I kill you now, the people will say that he saw a group of young men, latched on to them to say he's a brother & then he kills them.” The Egyptians would then conclude, Is there such a thing where a brother kills a brother; Yosef must have been lying.

Says רב זילברשטיין we that learn from this conversation that when someone wants to dispel bad feelings someone has towards him, he shouldn't just brush him off with lame excuses. He should instead get to the heart of the matter & explain why those feelings aren't founded. This is what the Torah tells us when Yaakov explains to Yosef why he buried Rochel on the road rather than in the city.
Rashi explains that he elaborated & told him, I didn't even bring her to בית לחם which I know has caused you to be upset at me in your heart. You should know, though, that I did it only because 'ה told me to. הגר"ח שמואלביץ asks, “why did Yaakov have to go into detail with Yosef? Why not simply say 'ה told me where to bury her? הגר"ח שמואלביץ answers that had Yaakov just said that, Yosef wouldn't have been satisfied & would always be thinking that maybe there was something more he could have done. Therefore, Yaakov went through the entire explanation with him including all the different angles as well as what he could have done in order to explain to him that even with all the questions you might have, Rochel’s burial followed 'ה's command. Therefore, he couldn't have any other thoughts on the matter.

Why does it matter if someone has lingering thoughts as long as you know that you did the right thing?

When the brothers asked Yosef for forgiveness, they said ועתה שא נא לפשע עבדי אלקי אביך ,so now, please forgive the spiteful deed of the servants of your father’s G-d.  Rashi says they were reminding Yosef that although your father is dead, his G-d is still alive  

The sefer עטרת צבי explains by quoting the gemara that says, at the time when a person is in pain, the Shechina says קלני מראשי קלני מזרועי , my head is heavy & my arms are heavy. I created this person & now he's being punished; the Shechina is pained by the suffering of people.
Yosef's brothers believed that, while Yaakov was alive, Yosef did not wish to cause him pain so he didn't harm them. Therefore they said to him, "although your father is dead, his G-d is still alive; if you didn't want to cause pain to your father surely you wouldn't want to cause pain to 'ה who shares in everyone’s pain.

The אוצרות התורה relates a story that was told to the חיד"א by the אור החיים who said that in רב חיים בן עטר זצ"ל's town, one of the prominent members of the community degraded a חכם. The rav called the חכם to appease him and convince him to make peace. As he's talking, the חכם interrupts and asks, “why are you are you bothering yourself with this? The second he insulted me, I immediately forgave him because the 'זוהר הק says that the sins of the Jewish people cause 'ה anguish. Had I not forgiven him right away, the sin would take effect causing pain to 'ה. Therefore I forgave him before the sin could even take effect.

Based on this, the חיד"א says that's why it says כל המעביר על מדותיו מעבירים ממנו כל פשעיו anyone who overcomes his character traits & allows things to slide is forgiven for all his sins. Since he lets things slide, forgiving people who harm him, he insures that 'ה not be pained;  מידה כנגד מידה , all his sins are removed so as not to pain 'ה

That's why it’s important not to leave any lingering doubt when you appease someone for we don't want people to be pained, thinking bad of other people thereby causing 'ה to be pained too. This teaches us to admit when we’re wrong & to explain the situation so that there is no bad blood which would cause anyone any pain. Then, מידה כנגד מידה, we too won't have any pain!