Yes and no....

Part of time is that not only does the past affect the future, but the future also affects the past.

By going back in time and taking note of the pickpocket, for example, you learn enough about him to file a police report, so you do so.

However, had you not gone into the past to discover what happened to your wallet, you have still changed the future, as you would not have reported it stolen had you not discovered it was stolen and not lost.

So, the pickpocket, having the same ability, upon getting arrested, travels back in time so that he does not steal your wallet...

Not having had your wallet stolen, you would never have reported it stolen. Now, we have a paradox, as the pickpocket no longer had a reason to go back in time and not steal your wallet.

So, no. you cannot avoid the paradox this way.

Yes and no....

Part of time is that not only does the past affect the future, but the future also affects the past.

By going back in time and taking note of the pickpocket, for example, you learn enough about him to file a police report, so you do so.

However, had you not gone into the past to discover what happened to your wallet, you have still changed the future, as you would not have reported it stolen had you not discovered it was stolen and not lost.

So, say instead, you were going to meet a friend for lunch, and in the future, that friend would have dropped his wallet, and lost it at your lunch. Now, he doesn't lose it...