I'm always over-worrying about my kid, family and of course my pets. So I just want to make sure my betta's fins are looking okay after coming home from the petstore a week later.

This was the day after he got into his 20 gallon tank.

Here's the best I could get. This was taken maybe thirty minutes ago.

It's very blurry >_< Sorry.
Anyway so I was thinking it looks like new growth but it looks raggedy to me.
Like I said, I think I'm worrying a bit too much but I wanted clarification so I would know in the future (sorry if it's just new growth and I wasted your time :< )
Housing
What size is your tank? 20g long
What temperature is your tank? 80
Does your tank have a filter? Yes
Does your tank have an air stone or other type of aeration? Only from slight surface disruption
Is your tank heated? Yes
What tank mates does your betta fish live with? One mystery snail
Food
What type of food do you feed your betta fish? Aqueaon Pellets (will pick up NLS after holidays)
How often do you feed your betta fish? 2-3 pellets, once in the morning and once in the evening, fasts one day.
Maintenance
How often do you perform a water change? Twice weekly
What percentage of the water do you change when you perform a water change? 50%
What type of additives do you add to the water when you perform a water change? Water conditioner
Water Parameters:
Have you tested your water? If so, what are the following parameters? It all came back in the "safe" range.
Ammonia:
Nitrite:
Nitrate:
pH:
Hardness:
Alkalinity:
Symptoms and Treatment
How has your betta fish's appearance changed? Less clamped, just a little worried about the ragged appearance of his fins.
How has your betta fish's behavior changed? He's friendlier. Hasn't rebuilt his nest since the filter's strong current before baffling destroyed it.
When did you start noticing the symptoms? Yesterday
Have you started treating your fish? If so, how? Nothing yet
Does your fish have any history of being ill? Not that I know of
How old is your fish (approximately)? Only had him a week.
Gah, after filling it all out I feel like I'm wasting your time D: I'm sorry!!