By deciding to work from home (joining such a team or asking the management for such an option), the person has to make sure the direct manager knows what value is being delivered.
Ask the management if a task tracking system is in use and make sure every assignment you receive gets its status updated while working from home.
In case no such system is adopted by the company, suggest your management you’d be sending reports (daily or weekly, depending on how long you are expecting to work from home).
The trust problem comes from uncertainty.
Expose your work and the problem will be solved.