The subject of prayer is not painful to me as it is for Screwtape, but I admit to being uncomfortable talking about it. This is partly because many Christians that enthusiastically talk about their praying habits are very often the sort of holier-than-thou types who inflict their religious practice on everybody unfortunate to have contact with them. However, it is also because it is such a private matter, that I feel rather naked about talking about it.
Prayers are said for different reasons: as a plea or call for help, to give thanks, to gain insight, to calm oneself and find peace etcetera. What it isn't is

"talking to a bearded man in the sky"

and while funny, these quips, if taken literally, only serve to reinforce misconceptions about an activity common to religions from Buddhism to Zoroastrianism .
Certainly prayer is a form of meditation as much as it is worship. I find it very beneficial and it seems studies have shown that it does have tangible effects. TThe neurologist Andrew Newberg's brain scans reveal that monks, priests, nuns and gurus alike have exceptionally focused attention and compassion sites.
It is interesting that Screwtape wants to direct us away from prayers which are regularized. This might come as a surprise because most criticism of bad prayers are "lip service" to "formulaic" prayers. Oddly, for Screwtape, hollow prayers are more easily achieved by manipulating, once again, our pride.
Kneeling and repeating phrases might appear to us banal, embarressing or silly. We might feel that we are pretending to be something we are not (which is ironically exactly what we are doing- and the point) or we might feel that it is elementary as if we are anything other than amateurs at prayer.
He wishes to exploit our vanity by encourage us to think of ourselves as devout and experienced at prayer as a monk or sister who spends every day for years in prayer and made it their
raison d'etre. This is equally absurd when a newly coverted Buddhist in Hollywood thinks that they can skipe the lotus position and the mantra and get straight to the business of transcendence.
Screwtape also suggests directing the prayers to a physical object: i.e. idolatory. Note that this does not have to be a golden calf or even a crucifix but merely "the corner of the bedroom ceiling" or inside his our head. Screwtape, rightly or wrongly, considers it almost impossible for us to know God while mortal but warns of the loophole of
humility: “Not to what I think thou art but to what thou knowest thyself to be”,
In fact Screwtape talks about our lack of humility being his opportunity: that we forget that we a physical as well as mental and spiritual creatures and that our physical actions do indeed affect our mental and spiritual aspects.