Autopopulate a value

I created an options page where users can enter their Google Captcha key and secret. Using update_option I am able to add these values to Elementor's settings.

I'm trying to do the same with JetForm but it seems to need these values actually added to the settings page. If I overwrite them with update_option the captcha option doesn't even appear on the form source code.

Is there a way to have my option's page settings actually appear in the fields for JetForm instead of just the database?