Repairing my husbands credit with goodwill letter?

My husband is applying for a home loan and he has a few late payments from earlier this year. So we wrote a goodwill letter to the company. Here is there response.
“This letter is conformation that a request to delete any delinquency that occurred since 12/01/2008 has been sent to the major credit reporting agencies”.
“Please retain this letter for future reference. We apologize for any inconveinence this may of caused you.”

So they are going to have the major credit agencies delete the negative items correct? I just want to make sure Im reading this right. We have had terrible luck lately and I hope that is what they are saying. If so, how long until we see it removed from the credit report?
Nothing is in collection the account has been on time for 5 years other than my husband losing his job for 3 months the begining this year. So we were late (but paid) january, feb., March. Then on time since April and paid in full.

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