The solution, though, will not be easy. Without support from EyeTV's 
side, Remote Buddy will have to go a very long way to detect whether 
this dialog is currently displayed. But that support from EyeTV's side 
may be coming. If not, I have added your entire post to the ToDo list, 
so it is not forgotten and will be looked at again on a regular basis.

In the meantime, here's a workaround:

1) Ensure your mapping at RB Prefs > Mapping > EyeTV includes the 
possibility to enter the Remote Buddy menu (which is the case with 
default settings).

2) Go to Prefs > Menu > EyeTV. There, drag the menu element located at 
"Actions > Virtual keyboard > Return (key)" into EyeTV's context menu.

3) The next time you experience the modal dialog problem, you can then 
open Remote Buddy's menu, select the entry you just added and dismiss 
the dialog.

Best regards, 
Felix Schwarz