macOS – How to Remember Window Position and Size

The problem you are having with Gitbox is because not all application are scriptable. Which means you cannot talk to it via applescript. What you can do for apps like that is use System Events to do some of it for you.

*Check if scriptable *

set theApp to "Gitbox"

tell application "System Events"

    set isScriptable to has scripting terminology of application process theApp

    if isScriptable then
        my scriptableApp(theApp)

    else
        my nonScriptableApp(theApp)

    end if
end tell
on scriptableApp(theApp)
    tell application theApp to get the bounds of the front window
end scriptableApp
on nonScriptableApp(theApp)
    tell application "System Events"
        set the props to get the properties of the front window of application process theApp
        set theSBounds to {size, position} of props
    end tell
end nonScriptableApp

Get the bounds via system events

#get the bounds via system events 

tell application "System Events"
    set the props to get the properties of the front window of application process "Gitbox"
    set theSBounds to {size, position} of props
end tell

Set the bounds via system events

--set theSBounds to {{799, 490}, {513, 430}} #This is a test line that will set the bounds list so you can see the set bound code working un comment to use it

#set the bounds via system events 
tell application "System Events"
    set size of front window of application process "Gitbox" to item 1 of theSBounds
    set position of front window of application process "Gitbox" to item 2 of theSBounds
end tell

Ask the developer of iTap mobile RDP to add that as a feature. Normally it is up to the application to keep track of its own windows.