Static lice is an outdated term - they are just called hay mites.
You will need to see your vet for diagnosis and to be given the correct, weight adjusted, treatment of ivermectin in the correct length course. That is three treatments with two weeks between each treatment to fully catch the life cycle of the mites.
Please do not be tempted to use a pet shop anti parasite treatment on spec. Such treatments are low dosed and not recommend - they are unlikely to properly treat the issue and instead may only suppress meaning the mites come back. Low dosed products also contribute to resistance forming.
The guide below explains about throwing hay away and cleaning the cage
1 Double-checking the gender upon arrival
- Sexing
- Pregnancies and surprise babies
2 When to quarantine new companions?
3 Vet visits
- Health check/registration upon arrival
- Reclaiming vet cost for newly bought ill guinea pigs
4 Common illnesses in new guinea pigs
- Ringworm
- Respiratory infection (URI)
5 List of guinea pig...