Back in September I believe a new lady moved into the flat below us. we were up early one morning (6am and getting ready for a trip away. At 7am I put my 2 year olds shoes on and he ran up our hallway) shortly after the lady below came up to complain about the noise - there was no music/tv. Just the 2year old wearing shoes (laminate floor but thick underlay) and myself and DH chatting/packing and the tumble dryer.
We apologised, explained it wasn't a usual occurrence and said we'd make sure we didn't wear shoes whilst indoors as well as look into runners at her request. She then said the tv noise is also too loud and affects her health... We don't own a tv
I do watch tv via my phone and the laptop sometimes but the volume wouldn't be able to go up as loud as an actual tv.
I have since taken to using headphones other than when the 2 year old watches the odd DVD in the daytime.
Today I receive a noise complaint letter from the council that was made on Tuesday morning... (When I was out swimming with the toddler) of course there would of been the time from 8am to 9am when I was getting him ready that day though...
I haven't yet been able to afford runners but have been extra conscious of noise from the floor, banned my child from running indoors (he used to enjoy cruising the hallway) and I put him to bed at the latest by 9pm and usually 8am. I don't get him up before 7am. I'm so paranoid I'm constantly listening to how much noise my own footsteps make and tiptoeing after/before 7-9 daytime hours. 
I don't know what on earth I can do more, previous neighbours didn't complain and I'm sure we used to make far more noise. I do live next to a flat which has 3 school age children and I hear their noise myself but it's nothing other than everyday noise certainly wouldn't class it nuisance so there is the possibility that noise is travelling from that property...
Or I suppose the small chance that the noise complaint didn't come from this lady at all? Seems very very unlikely though.
WIBU to put a note through her door? And how should I word it if I did?
I could understand if it was a complaint over a child tantrumming as they are frequent currently due to his age, or over him singing his lungs out but again it's not something I have much control over and I'm doing everything I can already to minimise noise 
I was thinking of something like:
Dear neighbour,
I understand you made a noise complaint, I can only apologise if the noise level is unacceptable to you but I have been taking these measures since you came up back in September and feel there is little more I can do. Im not entirely sure the noise you are experiencing is coming from our property considering this. I also do ensure any noise only happens between daytime hours. Please feel free to pop up next time the noise level is unacceptable to you as it may help me to identify what it is exactly that is causing you a problem and clarify if it is our property or not.
That said... I don't really want to drop my next door neighbour in it if it's her kids the lady is hearing. Should I speak to her also? Should I check with others if they're hearing too much noise from us??