Ranking on an inner page instead of homepage - keep up with that or delete it?

I recently optimized the homepage of a website for a certain easy keyword. The homepage received an A grade on Moz and SEOPressor and was well optimized for the keyword. I also spent money on buying a backlink package on the homepage for that keyword. The rankings then dropped a little after a while. When I searched manually for that keyword I saw that the website is actually showing up for that keyword but a sub-page of the website shows (not the homepage). The sub-page contains the keyword a few more times and even has the keyword in the URL. So what should I do in this scenario?

1) Delete the sub-page so that Google might show more precedence to the homepage? (Since Google usually only likes to show an instance of a website only once in the first 10 pages). Sounds stupid but the pros of doing this is that the homepage is stronger, older, and has more links than this inner page. It is risky though because I'm banking on the homepage to "take over" in the SERPs if I delete the inner page.

or

2) Stay with the inner page. Build links to this inner page instead. Optimize it even more than it is.

Any advice?

It just means your innerpage is more optimized for that keyword than your homepage.
This will happen quite often with your other innerpages.

Build more links to inner page. Than you will get rank for your keyword for sure dude...

Keep the inner page. Nowadays SEO should be focused more and more on inner pages instead of homepage.

Stick with the inner page. Google is telling you in plain English which page it prefers.

However, if you really want to rank the homepage instead then don't just delete the inner page, make sure you 301 it.

If you are going after the same keyword with your home page, you should reconsider using it there because of keyword cannibalism.

Stay with inner page,you will rank it more

Also use IFTTT and Video Linkwheels to Dominate and get more pages listed.