He looked at Mrs Tonks, wanting to apologise for the state of fear in which he left her and for which he felt so terribly responsible, but no words occurred to him that did not seem hollow and insincere.
"I'll tell Tonks - Dora - to send word, when she ... thanks for patching us up, that's for everything. I -"
Harry Potter and the Deathly Hallows
I don't quite understand the structure of the sentence, especially the that-clause. Is that-clause modifying something? What's the sentence saying exactly? Can we replace 'that' with 'which' in this case?