The easiest way is not to try to “type” into Tera Term, just use its macro support. From your DataGridView click event, generate a .ttl file like:
sendln "your command here"
Then run it with:
Process.Start("ttpmacro.exe", "myscript.ttl");
That’ll send the command straight into the right Tera Term session. If you don’t need Tera Term at all, just use SerialPort.WriteLine() in C# instead.