gamma Te - looks serious with an indifferent/strict way.
delta Te - looks serious with a displeased/unsatisfied way.
doesn't apply to all Te people, but this rule is true more often than not.
My theory is that it's asker/declarer dichotomy difference. Gamma Te sees things as they are and thinks that this is the way it is. they may be unhappy with how things are, but it's just a fact of life, nothing more. Delta Te starts wondering why and gets an inquisitive look.
Example - someone left the tap on.
gamma Te - "This is not good. Water was wasted."
Delta Te - "Did YOU leave the tap on?"
And even when delta Te types are quite happy with things, they still see some faults and they present it like questions and it's similar to blaming. Whereas gamma Te just states that some things suck and I can simply agree that some things suck.
Often people don't have to SAY anything to get the same result in the intertype relations. E.g. When either Te quardra type says "The tap was on", it will have different facial expressions. Gamma Te will look serious about it and delta Te will give a piercing look to the other person as if asking, "was it you?". And this is the vibe I get from delta Te types - it always feels like they're asking something and it gives them an inquisitive displeased look.