Learn Hardcore Japanese: watasi no meeru ni henzi wo site kudasai.

The particle に marks the target or recipient of the action. In メールに返事をする, you’re “making a reply to the email.” Although English treats “reply” as a direct object (“reply the email”), Japanese needs に here to show “to” or “for” that email.

Why do we say 返事をする instead of just 返事する?

返事 is a noun meaning “reply.” To turn it into “to reply,” you attach をする (“do a reply”). In casual speech you might hear 返事する, omitting the を, but the fully correct pattern is 返事をする (noun + を + する).

What does ～てください do here with して?

Any verb in its て-form + ください becomes a polite request. So 返事をしてください literally means “please do a reply.” It’s softer and more polite than the plain imperative 返事しろ.

Is there any difference between 返事をしてください and 返事してください?

Practically none in meaning. 返事してください simply drops the を, which is common in spoken or very casual Japanese. Including を (as in 返事をしてください) is more complete and slightly more formal, especially in writing.

Why is there no explicit “you” or “I” in this sentence?

Japanese often omits subjects when they’re clear from context. Here, the speaker (“I”) is implied by 私の, and the listener (“you”) is obvious as the one being asked. Adding あなた would sound awkwardly direct.

Could I use 返信 instead of 返事? What’s the nuance?

Yes. 返信 (henshin) is a Sino-Japanese term also meaning “reply,” especially for letters or emails, and is common in business. 返事 (henji) is native Japanese and more general (“answer, response”). In a formal email you often see ご返信ください or 返信をお願いします.

Why is the order 私のメールに返事を? Would 返事を私のメールに work?

Japanese word order is flexible but tends to put indirect objects (here 私のメールに) before direct objects (返事を) and then the verb. 返事を私のメールにしてください is grammatically possible but sounds awkward. The natural flow is “to my email” → “a reply” → “please do.”

How can I make this request even more polite in a formal email?

You can add honorific prefixes and use お願いします instead of ください. For example:
私のメールにご返信をお願いいたします。
Here ご返信 uses the honorific ご, and ～をお願いいたします is a more formal request than ～をください.