The Invoke-RestMethod should, in this case, be returning a PSObject. If you know the property name you should be able to access its value directly. If the property doesn't exist you'll get a $null value. You should also find the names of all the PSObject properties in the object if you want to verify whether the property exists regardless of its value.
What you've provided in your screenshots are the textual representations of the PSObject returned from two different instances of a PSObject.