That is an interesting situation and I am sure many others share a similar concern.

I would recommend trying out Podio (free), it lets you create all sorts of templates to capture and work with information (text fields, categories, dates, etc).

You can set it to receive e-mail for you and it will automatically insert the appropriate information into the fields (including attachments). You can decide if your staff only sees the name of the student and the attachment if you wish.

You can also create a workflow that informs you when your staff members finish the corrections and are ready to be sent back.

You can even use it to keep track of all pending essays, their progress and due dates so you are always on time.

Let me know if you have any questions!

Why would you ever hire someone you don't trust?

Well, it's certainly completely possible to build a system that would do what you're looking for, but I'd like to believe you can find something off-the-shelf that would accomplish it, since a custom system would definitely cost you more (e.g. thousands of dollars to get a decent system built by a reputable firm).

I'm guessing that the students are the clients in this setup?
One thing to watch out for is that if the student/client includes their name and/or contact information on their essay, then you (or the system) would ideally sanitize that information out of the essay before sending to the the teacher/employee.

I don't know a system that I'd recommend for this, but I hope that someone else is able to recommend something that you like.

A software has risks, apart from interrupting with other software installed in the computer it also gives easy access to hackers and hacking activities. I will suggest you do it legally.
An employer’s ability to monitor emails sent or received on an employee’s personal, web-based account is more complicated. In general, this type of monitoring is more likely to be allowed if the employee is using company equipment and has consented in writing to the employer’s monitoring of all computer use. Employee privacy in electronic communications is a complicated and still developing area of law.
You can read more here: https://www.nolo.com/legal-encyclopedia/email-monitoring-can-employer-read-30088.html
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath

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Here are some software options you can consider to help prevent employees from accessing your clients' email addresses:

Microsoft Office 365 - Microsoft Office 365 includes access control and data loss prevention (DLP) features that can help you prevent employees from accessing your clients' email addresses.

Symantec Data Loss Prevention - Symantec Data Loss Prevention is a comprehensive software solution that includes access control and DLP features, as well as email encryption and monitoring capabilities.

McAfee Total Protection for DLP - McAfee Total Protection for DLP is a software suite that includes access control, DLP, and email encryption features, as well as email and employee monitoring capabilities.

Forcepoint DLP - Forcepoint DLP is a software solution that includes access control and DLP features, as well as email and employee monitoring capabilities.

Proofpoint Email Protection - Proofpoint Email Protection is a software suite that includes email encryption, access control, and DLP features, as well as email monitoring capabilities.

If you are hiring online or remotely employees, I think you are right you shouldn’t trust anyone and you should apply software, yes there’s a software is DLP it makes you only control who can access your clients mail.. instead you can hire trusted local employees without using any expensive software