This is an idiom meaning that she was possessed by the unclean spirit. AT: "was possessed by an unclean spirit" (See: [[rc://en/ta/man/translate/figs-idiom]])
# fell down
"knelt." This is an act of honor and submission.
# Now the woman was a Greek, a Syrophoenician by descent
The word "Now" marks a break in the main story line, as this sentence gives us background information about the woman. (See: [[rc://en/ta/man/translate/writing-background]])