Assuming that the primary field of your linked table allows data to be written to it, you have 3 choices when posting your data to your linked record field:
You will either need to:
(1) Not send any data to that field at all,
(2) Create a “null” record in your linked table that your linked record field can link to, or
(3) Enable the “typecast” parameter in your API call, which will automatically create the “null” record in your linked table.