REST API Call for Programs "Used By" a Custom Object Field?

Looking to remove some fields from a Custom Object that we use primarily for demographic data. The issue is that any attempt to delete throws an error message that reads "Not able to complete your request. Please refresh to check if the object was updated by another request."

I'm assuming this means the field is still in use in some case - but the issue is that the "Used By" section doesn't load. Likely because we use this object in some form on almost every Program in Marketo.

Is there a REST API call to get a list of Programs that have a specific Custom Object field being used? I tried looking but it all related to Custom Fields and not Object fields.