The real reason there was never a farewell scene to Liz Shaw was because Barry Letts considered the character "unsuitable" and did not renew Caroline John's contract.
Liz could not properly bid farewell to the Third Doctor when she left him to return to Cambridge, as she was overcome by emotion. She was only able to say goodbye when she was out of earshot and the Doctor turned his attention away from her. At the same time, he was saddened to watch her to walk away and distracted himself from melancholy by playing with a caterpillar. (PROSE: The Scales of Injustice)