Date: September 29, 2010 12:35PM
I'm not 100% sure about these details, but I think it used to be that if a divorced woman, sealed to her first husband, wanted to remarry, she essentially had to get her ex-husband's permission to cancel the original sealing. If he didn't consent, I think he could be overridden, but he did get asked.
By contrast (and this part I'm sure of), if a divorced man wanted to remarry, they just sealed him to wife No. 2, without any input from wife No. 1.
I think it was back in the 1980s when they changed this to give the illusion of a little more parity for women. So after the change, women were allowed to express their reasons why their ex should not be allowed to be sealed to wife No. 2. It doesn't give Ex-wife No. 1 veto power over the second marriage, but it makes her think that at least she has some say in the matter, as ex-husbands used to have some say in whether or not ex-wife could be sealed to husband No. 2.
As for questions about whether the ex is current in spousal and child support, that is a temple recommend interview question, and a negative answer from ex-wife could result in ex-husband not being able to get a recommend, thus preventing the sealing. Of course, if ex-husband told the bishop that ex-wife was lying, he'd probably get the recommend anyway.
When these letters wind up going out to ex-Mormons, they are particularly obnoxious, as some here have already posted. I guess that some Mormon women get some feeling of comfort or control if they get asked, in a way that partially corresponds to the way men get asked, about an ex-spouse's remarriage.
The whole thing is stupid anyway, but IMO, this is how the current policy came about.