Hello,
Thank you for your interesting question.
You can identify the customer to be the pet owner and what they go thru with an existing solution. What are their steps before and after washing (or cleaning) of these clothes? If it is possible, you should visit a customer in their own place and make them walk through what they do to clean the pets' clothes.
If visiting them is an issue, next best is to interview them and the next best alternative is to call them up and ask them walk through the steps. Still nothing beats a field visit.
Once, you have observations from these and their emotional ups and downs (I know, this is a lot of work and typically may take weeks in some cases). then proceed to the generating How-Might-We (HMW) questions from your observations from the field. Now, embark on the multi-why analysis.
Hope this helps
Thanks and have a great day!
Bala