@Cat43I'm no expert on this as I've never actually made a claim, but nobody else has replied yet ....
I've read through the security deposit and Host Guarantee information and terms .... I'm not sure, but it looks like Security Deposit and Host Guarantee are different things .... the way it looks to me is that you claim on the security deposit within 14 days, and if you don't have any luck with that, then you claim on the Host Guarantee within 30 days ....
This is a page about the Security Deposit claims process - https://www.airbnb.co.uk/help/article/352/what-happens-if-a-host-makes-a-claim-on-my-security-deposi...
And this is a page about the Resolution Centre - https://www.airbnb.co.uk/help/article/767/what-is-the-resolution-centre
Did the process go through as described in those 2 pages?
This is the page about the Host Guarantee - https://www.airbnb.co.uk/terms/host_guarantee
Bottom paragraph in Section I says any amount payable is reduced by any amount received from a security deposit
Section II includes a definition of Covered Losses as "“Covered Losses” means and is limited to direct physical loss or physical damage to a Host’s Covered Property caused by the Responsible Guest "
I'm wondering if this is an issue with wording .... you said "I went to the resolution centre and asked for £100 to cover the insurance excess" ..... according to the terms of the Host Guarantee, damage to the carpet should be covered (as that is physical damage), but an insurance excess will not (an insurance excess is not a physical thing in your property) ....
Might be worth replying to say "I am claiming for damage to my carpet, which is a Covered Loss as per the terms of the Host Guarantee" ....
Take note of Section IV which says "Within thirty (30) days after you have incurred a Covered Loss, you must ...." which tells you what to do ...
I don't know if the above is correct or not, but that's how I read it .... maybe someone else will reply later to help out .... good luck with it and let us know what happens!