Using the Order API in either SOAP or REST mode with XML returns the payment's `additional_information` in an unidentified list, an array of strings without keys:
<additionalInformation>
<item>0</item>
<item/>
<item/>
<item>Credit Card</item>
<item>1</item>
...
These values are fairly useless and should be identified with something like this:
<additionalInformation>
<save>0</save>
<acceptjs_key/>
<acceptjs_value/>
<method_title>Credit Card</method_title>
<response_code>1</response_code>
...
The keys are being stripped by the Magento\Framework\Reflection\DataObjectProcessor, though I don't think that is the real cause as I was not able to change the way this data is sent.