A few suggestions for doing grid interpolation with MapInfo Pro/MapBasic
In MapInfo Pro without add-ons gridding is part of the thematics. But you only have a few interpolation methods to pick from, TIN and IDW.
To get a look at the MapBasic code, try creating a Gridding Thematic using MapInfo Pro or have a look at the Create Grid statement in the MapBasic help files.
Vertical Mapper is the gridding tool used for decades with MapInfo Pro. Vertical Mapper also comes as a SDK giving you the opportunity to write your own gridding application.
Vertical Mapper has been and still is used in a broad variety of industries from telecom to engineering companies.
Discover has been developed by the Australian company Encom, now part of Pitney Bowes, with a main focus on the exploration and mining industry. Discover has however also been adopted widely within other areas such as geotechnical companies and public sector.
Discover, however, doesn't come with a SDK so you are not able to create your own applications.
MapInfo Pro Raster x64
The new kid in town is called MapInfo Pro Raster. So far Pitney Bowes has only released a beta release but the first release is expected late April or early May.
The first version is focused on importing and working with existing grid files. The second release later this year will also be able to interpolate new grids.
Also notice that MapInfo Pro Raster is a 64 bit application that requires MapInfo Pro 64 bit to work.
We also release a .NET based SDK for MapInfo Pro Raster. This will make it possible for you to create your own grid application, either as a stand-alone tool or as an add-on for MapInfo Pro x64.
If you want to get started with the .NET SDK for MapInfo Pro Raster, have a look at this article: Developer Dojo: Getting started with the MapInfo Pro Raster API