While you can delete features with Arcade, doing so in the Field Calculator is complicated.
If you want to build a model, you can do this easily with the available ArcGIS Tools:
In the Select Layer By Attribute tool, use this SQL expression (this works for a file gdb, you might need a different expression if you work in an enterprise gdb):
TextField = 'Completed' AND DateField < CURRENT_DATE() - 30
Have a great day!
Johannes