Change state of menu-items in scene 1

Sure.  

Create a T/F variable for each scene. On the last page of each scene create a trigger to set the variable to True. Be sure to place the trigger BEFORE the trigger to jump to the menu slide.

Set variable Item2 = T when user clicks [object to return to menu]

Jump to menu slide when user clicks [object to return to menu]

On the menu slide, place these triggers (one for each menu item):

Change menu item 2 to Completed when timeline starts on this slide if variable Item2 = T

For each menu item, edit the states duplicate the Normal state, creating a new state named Complete. Paste or create the tick on Completed state.

There is a sample that illustrates how here: https://community.articulate.com/discussions/articulate-storyline/free-sample-restricted-and-free-random-navigation-using-variables-and-triggers 

It uses slides, not scenes, but the principles are there. You may want either the mixed or restricted version.