Thinly slice the squid bodies and halve the tentacles.
Combine the pure olive oil and garlic in a large skillet and cook, stirring, over medium-high heat until golden brown. Add the chile and squid and cook, stirring constantly, for 1 minute.
Transfer the squid to a bowl and mix with the extra-virgin olive oil and vinegar. Season with salt and pepper. Marinate the squid in the refrigerator for at least 1 hour or up to 3 hours.
Remove squid from the refrigerator 30 minutes before serving. Add celery leaves, parsley, and olives and mix to combine. Season with salt and pepper. Divide among plates and serve.