Well, if they officially don't provide the data via API you don't have much options. Tell your client it's not possible to get the data they want via API. They should ask Quill's account representative and/or support to put it on their roadmap.
There are other ways, like screen scraping and reverse engineering private APIs but I don't recommend that. It is likely against Quill's term of use, these solutions tend to be very brittle, and they could get your client into a trouble.
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Well, if they officially don't provide the data via API you don't have much options. Tell your client it's not possible to get the data they want via API. They should ask Quill's account representative and/or support to put it on their roadmap.
There are other ways, like screen scraping and reverse engineering private APIs but I don't recommend that. It is likely against Quill's term of use, these solutions tend to be very brittle, and they could get your client into a trouble.