Despite that is a phrase of despite.
Here's a list of synonyms for despite.
In spite of the given clause
“Despite the work he had to complete, he went on a holiday anyway.”
(rare) Evil feeling
“She acted out of despite with no thought of the consequences.”
(archaic, obsolete) Contemptuous feelings or actions
“His despite for the king was apparent.”
(rare, dated) Detriment or disadvantage
“I know of no government which stands to its obligations, even in its own despite, more solidly.”