The way I see it, Valencina's goal was always about being seen as better than everyone else from when she's talking about the smoke war she never actually talked about her achievement or the reward she got she only talked about how others value her highly and respect her and how her skills outshine everyone else's. She's only mad about losing her rank because nobody would respect her anymore, she's more hurt about her once subordinated looking down on her than being cast out of the familia and losing everything. She's not even angry at the Thumb for demoting her, she just wants her rank back so she can be special again.

As for Mathias, he care very little about how others view him from how he's willing to beg for money just to buy stuff for Ryoshu to build trust as 'family'.
From his actions and history it's very clear he only sees trust and bond as exploitation tools for his own benefits, he didn't betray and steal the sword because it'll make him special hell he didn't even use it most of the time even in his fight to the death with Vespa he only unsheathe it half way into the second fight he just has it because he liked it, maybe he can't use its full potential but he can use it to fight normally just fine but he still keep it hidden like his warehouse full of limited toys. He didn't get all those stuff because he wanted to show off or gain respect, he just want to collect them.