He said he would vouch for me if I wrote a letter of apology to management.

他说如果我给管理部门写一封道歉信，就会保我没事。

youdao

For example, when we have quarrel with our friends sometimes, we can explain or apology to them by writing a letter.

例如，当我们与我们的朋友吵架的时候，我们可以给他们写一封信来解释或道歉。

youdao

He said that he had written a personal letter to Bush after the debate asking for an apology but had not received a reply.

CNN: Ex-Russian prime minister wants apology from Bush

He has written a letter of apology to the Pope and has already asked for a pardon.

BBC: Vatican embarrassment as Pope's butler goes on trial

Before negotiations ended for the week, on March 22nd, the school agreed to issue a letter of apology, according to two people familiar with the talks, and also to remove a number of emeritus trustees, some of whom had been on the board when abuse was reported.

NEWYORKER: The Master