# make a good impression

"cause others to think well of them" or "cause others to think that they are good people"

# in the flesh

"with visible evidence" or "by their own efforts"

# to compel

"to force" or "to strongly influence"

# only to avoid being persecuted for the cross of Christ

"so that the Jews will not persecute them for claiming that the cross of Christ alone is what saves people"

# the cross of Christ

These words are a metonym for faith that Christ died on the cross so God would forgive his people's sins. Alternate translation: "believing that God forgives his people's sins because Jesus died on the cross" (See: [[rc://en/ta/man/jit/figs-metonymy]])