It is a sporting button and was worn on hunting jackets of the time. I would date it mid to late 1800s. I think it is actually a wolf. And, I don't think it has much monetary value. But, it is a nice find and I would be proud of it.
Unbelievable how even google on this browser doesn't yield the same results as I had on my cell browser. I found a site with similar buttons but nothing exact. There were greyhounds and rabbits and foxes. Are you sure the pic doesn't depict a fox seeing as it is about sporting? They too have the flared 'mane' behind the head. I only say this because the site didn't have any wolf buttons but had quite a few fox buttons, granted I do acknowledge the fact this button was not on the site which means some types may exist even tho they are not on the site. Time frame tho late 1800s. After the civil war as there are many CW buttons with the 'Extra Fine' printed on the back.
It is not the same as your button but the button in this link is a wolf's head. https://www.etsy.com/listing/204498708/wolf-head-sporting-button-of-brass-19th
And, if I read it correctly, the "Extra Quality" backmark was used by the Steele and Johnson company. They were in business from 1852 until 1920 when the Waterbury Button Co. bought them out.