This is a shared problem between creating tickets over the Desk API as well as using the built in editor to edit tickets.

Say you have a ticket and want to edit its contents to:

Then only ⏩ will render correctly after you save the input. The other emojis will be replaced by question marks:

Same thing happens when I try to create a ticket over the Desk API using the same string as above and transmitting data as JSON / UTF-8 (Content-Type: application/json;charset=UTF-8).

And as I just noticed, this support forum seems to have the same issue, except that there are no question marks to replace the emoji. They're just gone. This is the original input:

Smileys: ⏩

As you may see, the emoji got replaced with... nothing.