Ultimately, this is mostly irrelevant due to how weak the Goblin Trapsmith is, but it's good to know nonetheless.

The Warrior gets to roll two dice in battle and use the higher attack roll.  The Goblin Trapsmith forces you to roll one extra die for your attack roll and use the lowest result.

How many dice does the Warrior roll against the Goblin Trapsmith and which result does he pick?

Does he still roll two dice?  That seems to negate the Warrior's ability to roll extra dice.

Does he roll three dice?  That seems to match the language of the card, "Roll one extra die."

Does he roll four dice?  That would be two dice for one of his attack rolls and two dice for the other.  That seems to be a bit of a stretch, but within the realm of possibility.

And then which result does he pick?  His special ability lets him pick the highest.  The Goblin Trapsmith says he must pick the lowest.  I know that there's an priority to these things and that it's in the rule book.  I'm short on time at the moment, so I'll accept that some people will probably yell at me over this.

This came up in our game last night and we were trying to figure it out until my wife realized that she had strength 7.  Against a strength 1 she cannot lose.

Q3: Can the Warrior use his special ability when he fights
the Goblin Trapsmith?
A: No. The Warrior must roll two dice for his attack roll and
use the lowest result.

This is from the V1.1 FAQ. They don't go into why it has beeen decided to go this way, but it is official. I can only assume it has to do with the Warrior ability being a "May" ability, which implies it is optional vs. a "Must" ability which is not optional. Alternatively, the Warrior ability is a "Can" statement, whereas the Trapsmith ability could be construed as "Cannot" choose to roll normally, and must roll 2 dice and use the lowest, in which case the "Cannot" trumps the "Can". Either way, it isn't clear just using the rulebook, hence the FAQ answering this one.

Thanks.  Could you post a link to the FAQ?

Goblin Trapsmith

Q3: Can the Warrior use his special ability when he fights

the Goblin Trapsmith?

A: No. The Warrior must roll two dice for his attack roll and

use the lowest result.

http://www.fantasyflightgames.com/ffg_content/Talisman/support/faq1-1/Talisman%20FAQ%201-1.pdf

It's not such a clear case from the basic rules but I expect it's because the "Positive" warrior ability (Can) is overuled by the "negative" effect of the Goblin (Cannot) as was mentioned above.