Those letters are his heart and soul - and Gulaal does need to read them coz that one of the main reasons to understand Kesar and connecting the dots in what happened when he left, and the lead up to it and how he kept himself away and never sent his letters, and when he came back - still full of anger and so on, and how he has been, and how he has been with her and also D... and what he has been thinking and how he has made many assumptions and so on
Its these letters will make her realise the depth of Kesar's anguish and truth he has kept buried in him for years with pain, anger and hurt, until Gulaal doesnt figure out the root of Kesar problem and his being due to how he is, she cant fully get and understand Kesar's emotional turmoil, coz that why i feel there is restrict on them not making Gulaal fully understand Kesar yet
Kesar did say in one his letters, he cant even bring the words on his mouth to even ask, one out of fear to hear the truth and one that its so buried in him, that he doesnt even know how to get it out and some of it comes out in little riddles and hints