Podarilo sa mi to opravit.
Riesenie je kompilaciou roznych zufalych rad z internetu, takze nie je to nikde takto pokope napisane ako to teraz napisem tu:
1. Uviest mac do Recovery modu: pri restarte drzat command+r
2. V recovery mode spustit terminal a zadat prikaz na vypnutie System Integrity Protection: csrutil disable
3. Restart do normalneho rezimu, otvorit terminal:
sudo /usr/libexec/PlistBuddy -c "delete:add-app" /System/Library/CoreServices/Dock.app/Contents/Resources/com.apple.dockfixup.plist
sudo /usr/libexec/PlistBuddy -c "delete:add-doc" /System/Library/CoreServices/Dock.app/Contents/Resources/com.apple.dockfixup.plist
zmazat apky z doku. Po dalsom restarte sa uz neobjavia.
Volitelne: V recovery mode znovu zapnut SIP: csrutil enable

edit: pozeram, ze podobny postup je v 2. linke, co si pisal. Akurat typek nedodal info ako vypnut SIP.