Mikasa has recieved subtle development throughout the manga, but she is still in some respects the same person at heart i.e., she hardly vocalizes her feelings, it's always sort of something like >you secretly mean a lot to me so I will try my best to stay by your side and protect you. She couldn't even tell Eren what he really meant to her, what the scarf meant to her and why she had been by his side all this time. But these are the things I believe she will eventually be able to resolve.
Some people argued that Mikasa was useless and didn't even understand what was going on, but even though she may be the most quite one, she is not dumb or inattentive of her surroundings. She was the only one to show us, in the midst of this chaos, that Eren was a kind, vulnerable, sweet boy lost somewhere in the cruel world... She realized her misconceptions about Eren and is again gradually moving to another potential milestone.
I read her interaction with lousie as another form of subtle development, which will likely play a role later. Lousie represents the idealistic, young and naive side of Mikasa. After Eren's harsh words, Mikasa is more aware of this and Lousie serves as a constant reminder of that.
Lousie tells Mikasa that she kept the scarf, because this way she could feel closer to her, which is something Lousie very much desires but can't have. The panel on the left suggests that Mikasa feels pity for Lousie and possibly for herself, because she also wanted to have that same sense of connectedness with Eren.
Mikasa kept the scarf to cherish the kindness, hope and affection eren showed her, but possibly also because she thought that through the scarf, she could always remain closer to Eren.
When she says all she wants is to be close to Eren, she really reminds me of the lousie we saw this chapter. Like Lousie, Mikasa was also clinging to the scarf, because it allowed her to remember her cherished one.
I understand Mikasa and Eren's relationship is much more deeper and significant than Mikasa and Lousie's, but nonetheless there are some similarities. It's like isayama is trying to rid Mikasa of her naive and hopeful side through introducing lousie, so she could have a more mature and logical connection with Eren. So that next time Mikasa sees Eren, she can really be honest with him and also rational about their relationship and his actions (without her feelings preventing her from doing so).
Unlike Lousie, Mikasa became a soldier to protect Eren, but she also looked upto him. Her Eren was perfect, kind to even his enemies, simply someone who was capable of only good things, but in chapter 123, she realized that she had been lying to herself all this time.
This panel of Mikasa walking away hints that she has realized this idealisitc and naive part of her existence (what lousie says here is what a younger Mikasa would have said to eren, in a similar situation) and she is finally willingy to move forward. Moving ahead is not riddding herself of the qualities of love, affection and loyality, but it's about the acknowledgement that sometimes the good and admirable qualities can blind one to seeing the truth about oneself and others.
