It's interesting that 気にかける is used, which is like 気になる but lean more into the "look after" and "concern" kind of care. Basically it says he does have concern about Kougyoku but can't help teasing her. It's sweet that his descriptions are "the one who supports her dream" and "providing her consultation and talking with her in the imperial palace". And that gives a little more context to this tegaki.
It means he's genuinely trying to cheer her up here, but being an avoidant asshole with nonexistent emotional intelligence makes him unable to express himself without cracking jokes or being a dick to hide his vulnerability. Yet it's still shown. Judar's not the type to take shit from anyone, not even Hakuryuu, and he retaliates every jabs thrown at him. But everytime Kougyoku starts throwing things in a fit of anger (that he caused), he just takes hits without even activating his borg. Everytime Kougyoku steps into the picture Judar becomes visibly gentler. They have few scenes together, honestly it's not their fault the Haku-Ju-Kou group were confirmed to be the secondary trio right before the last arc and had to share every possible screentime with Sinbad's end of evangelion plan (also Ohtaka's tendency to shove her female characters sideline but I won't be talking about it), but all of them present that Kougyoku is also very dear to him.
