Current REST API Does Not Support Managing Pre-defined Tags/Values for Custom Fields

What we currently have is a Custom Field for Features with a type of "Predefined tags field". Within that custom field, we have several dozen pre-defined tags/values which have been added via your Web UI. They work as expected with Features.

What I can't find is any documentation on a REST API that will let me query or manage that list of tags/values.  I reached out to support and they confirmed that managing those values isn't something in the REST API.  So....I'd like to request that ability.