I don’t see that reducing her hours would ever give her more money if her tax code is correct. Yes she’s taxed on her salary income, but never more the income itself.
To have a take home of £1000 sounds like she was earning approx £12500 a year, so pretty much zero tax, as £12500 is the basic rate tax threshold.
As she now has an income of approx £21850 (assuming full “new” state pension) she’ll have approx £155 tax to pay, plus approx £30 NI (no NI on the pension). So that fits with the £800+ that you mention. But… that’s me assuming she gets a full new state pension. So first thing to do, is make sure her tax is correct.
Reducing her hours won’t increase her money - just increase the amount per hour she has take home.
She could look a paying into a pension!
She could set up a private pension and pay in £2880 per year. That will be topped up automatically by tax relief to £3600, which is allowed under 75.
So she could take £1800 out of her state pension each year to top up her “missing” months of £150 a month tax payments.
But at the same time, pay £2880 into a private pension and have it topped up to £3600, gaining back £720 of it.
That figure of £2880 is the maximum that a non tax payer can pay in, but you’d have to check it’s still OK in her earnings situation.
There are rules about “pension recycling” but as she’s still earning I think it would be fine.
Of course, once in the private pension it becomes taxable once drawn out. But… the first 25% of each withdrawal is tax free, and her state pension plus the rest would be under the £12500 tax threshold - once she stops earning.
Definitely check it out in more detail don’t rely on what I’ve said… a great place to check with those more expert than me is the pension forum on moneysavingexpert. The £2880 > £3600 is really well known, so you should easily get an answer there!