Should I use Google, Grammarly, spellcheck or a dictionary when writing an essay for the correction service?
No.
You shouldn't use Grammarly, spellcheck or a dictionary when you're writing an essay to submit to the correction service. If you do, you won't learn your real level and your real mistakes.
Don't use Google either to help you generate ideas. Treat the correction service like test practice. You can't use Google in an actual IELTS test, so don't use Google to practice for the test.
When we say to CHECK your work, we mean you should proofread.