en_tn_lite_do_not_use/act/22/05.md

can bear witness

"can testify" or "can tell you"

I received letters from them

"The high priests and elders gave me letters"

for the brothers in Damascus

Here "brothers" refers to "fellow Jews."

to bring them back in bonds to Jerusalem

"They ordered me to bind with chains those of the Way and bring them back to Jerusalem"

in order for them to be punished

This can be stated in active form. AT: "in order that they may receive punishment" or "in order that the Jewish authorities could punish them" (See: rc://en/ta/man/translate/figs-activepassive)