Oes T.S. Eliots poetry have trouble with women? (Hell want to know what you done with that money he gave you? To get yourself some teeth TWL.II)

Please scan through Eliots poetry but focus on Ash Wednesday, A Game of Chess, Hysteria, Portrait of a Lady

For the secondary sources please consider the following essays by Eliot: Dante, Ulysess, Order & Myth, The Metaphysical Poets, Marvell,Reflections on Vers Libre, Laforgue, Hamlet and any relevant biography on Eliot.

Id like to include his own theory on writing e.g. the Objective Correlative to analyse his poetry, particularly in relation to women and the quote attached to the question. Hence come to a conclusion on this question of whether or not Eliot has a problem with women.

Please include as much secondary reading as possible.
Im attaching some Poems and essays that may be useful and already mentioned above.