in simple terms, textual intergrity is the VALIDITY of the text (the criticism)
e.g. how valid is the christian reading/interpretation of Lear? is the christian interpretation contradictory itself?
consider the validity of the Christian reading,
when Gloucester says,
As flies to wanton boys are we to the gods; they kill us for their sport
or
'the gods are just, and of our pleasant vices make instruments to plague us.' and
'This judgements of the heavens, makes us tremble, touches us not with pity'
and also,
when Albany says, 'the god defend here!' and the next line, Lear enters with Cordelia (dead) in his arms?
here's just something to think about