The exact meaning of invoke can depend upon its context. For example:
"invoking God's help"; or "invoking the spirit of the dead" — to call upon a great or magical power
"I invoke the First Amendment"; or "I invoke the words of Thomas Jefferson" — to cite or call upon for validation
"She invoked his sympathy and family memories." — to call upon someone's feelings or memories
"She invoked his assistance." — to call earnestly for
"The program invokes the subroutine" — to call up a computer program
In the early days, during those conversations where he had felt himself to be at sea, surrounded by people wealthier and better connected than he would ever be, by people utterly at ease in the world he was so desperately trying to join, he would sometimes allude, though never directly, to a distant but important lineage, invoking false ancestors to stand behind him and lend support.
There are no more uses of "invoke" in The Memory Keeper’s Daughter.