Programmatically Append Rows to a Table

I am curious if there is some way to add rows to a table created in TablePress using php. I use Zapier and would like to create a scenario where some action in another app triggers a Hookpress call that can then hook into TablePress and create a new row in an existing table, populated from data supplied to Zapier by the other app.

I understand this lies outside the scope of what you can do for support, but if you have any suggestions for a starting point, they would be appreciated.