Traveler Theme has support an Affiliate demo which allows users to integrate some OTA system in Theme, you can check on our demo here:
With this affiliate system, you will able to add those API in Traveler Theme and your customers can make the search form in website. Then, the booking process and payment method will be directly to those selected API system.
Basically, our Traveler Theme support for search form only, we do not control or manage any database from those system.
Hope it clears and help for you all.