causing offence

If your initial "Oh sorry! I didn't recognise you for a moment!" didn't satisfy her than I doubt anything will. It doesn't sound, from what you've said, as if you did anything wrong. Let it go.

If you've told the story straightforwardly, you did not 'cause' offence; the other person took offence.

Thank you. I'll just wait for an opportunity to put things right.

You tried to explain ... you went to her home she wasn't in ... leave it there ... you have tried, don't let it worry or get to you.

If you didn’t avoid her on purpose then you ve done all you can to explain
My eyes are bad and I ve told people to always speak to me first as I may not see them
You can only apologise so much, sounds as if you’ve done that there’s nothing more to do

Some people are in the business of being offended.

cooberpedi

Thank you. I'll just wait for an opportunity to put things right.

I honestly do not see there is "anything to put right".

You failed to recognise a friend, who took offence and has not accepted your apology.

Leave her to come out of her huff. She is being quite unreasonable here.

To me this is a clear case of "Least said, soonest mended."

Do please stop beating yourself up about a very ordinary occurence.

We all sometimes fail to recognise or greet someone, and as your sight grows poorer when you age, you will probably from now on frequently fail to see someone or other.