We ought not to grieve or become irritated at anything because, by frequent vexation and irritability, we form the morally and physically very injurious habit of irritability, whilst by bearing opposition with equanimity we form the good and useful habit of enduring everything calmly and patiently.
If you wish that God should speedily give you hearty faith in prayer, strive with all your heart to speak and to do everything in regard to other people sincerely, and never be deceitful in your dealings with them. If you are straightforward and truthful with others, then God will give you straightforwardness and sincere faith also in reference to Himself.
You ask for some way of completely eradicating irritability. The inclination to irritability is given us to use against sin, and we were never meant to use it against our fellow men. When we do, we act contrary to our true nature.
