I would say those are two different pairs of boots.
What you are describing is a network problem.
To keep a few things apart:
Grafana is responsible for the visualization and is/has no database itself, but can generate the desired visualizations from many databases (e.g. InfluxDB). Grafana therefore needs at least one database as a source.
- I assume you use InfluxDB, otherwise you would not ask here.
Telegraf is the data collector agent, which collects data from different sources and pushes them into InfluxDB. Telegraf itself is/has no database.
The mentioned three components can run on the same machine or on completely different machines, if needed these components can be scaled. How to orchestrate these components and build an architecture now depends very much on the individual use case.
In this case, I would reverse the direction. I would have the clients send the monitoring data to a central InfluxDB instance (or via a proxy).
On the clients I would run a Telegraf agent, which takes over the pushing of the data.
Or a separate script with an InfluxDB client library.