My first thought was to remove the selection dropdown, but it's true that it could be a good idea to keep it.
The problem I found was not how to use the dropdown but how to identify what is what when you have four elements side by side in an smartphone screen. That's why I believe that a small button wouldn't be useful, because even opening the dropdown itself is not easy at all. See an screenshot here:
https://imgur.com/a/npX4ewS
Instead, to use the space better, I would say that 'transforming' the open-end field into the dropdown rather than keeping both visible would be a solution. If the respondent select 'Other', the field allows them to enter a new response as it does now.
I would like to make it clear that the current behaviour is more than satisfactory, it's only the use of space on mobile *when a wrong answer is trying to be submitted* which is not optimous, I would say.
For now, I found a solution giving as less space as possible to the 'Country:' label on the left as well as the residual option 'No answer' on the right and keep the central column as dynamic. This way, the question displays better and it is usable.