She was a liability as well as stolen company property and needed to be brought in for decommissioning.
Weapon-X is dead, long live Weapon-X
If you recall, the Weapon-X program was declared a failure and shut down, so all of its current subjects were to be decommissioned and disposed of. This was the main reason that nurse Gabriela and the other staff conducted the mass breakout with the clone-mutant children.
Transigen wanted to concentrate on their new direction for Weapon-X; X-24.
Laura (along with the other mutant-clone kids) were declared as unsafe and compromised, a broken arrow so to speak. Not only that, but they were considered as "stolen company property", needing to be retrieved. It was Pierce's imperative to bring her in to ensure the safety of the public, as well as the safety of secrets which the Weapon-X program had.
Logan, the troublemaker
It all fell apart when Logan (and Professor X) were thrown into the equation. Retrospect is absolutely moot in situations like these; Pierce was not expecting to have so much trouble bringing Laura in. He seemed pretty at ease and confident in his and his team's ability to capture Laura (after all, they have had a very good success rate to date). Logan was having none of it though. Things simply escalated:
- At first Pierce was just following trails and leads
- Bumps into Logan, but only coincidentally as Logan was seen with nurse Gabriela
- Approaches Logan when he realises Laura must be harboured at the hideout
- All hell breaks loose
He doesn't have the benefit of hindsight, unfortunately.
Pierce is just doing his job
Pierce is a soldier (of sorts). He's under the employ of Transigen; whether he and his Reavers are mercenaries or fully employed by Transigen is unknown. He's been given the order or job to bring in Laura and wrangle up the rest of the children. He has no reason to stop even when things got really complicated and dangerous; especially given that since he's still around, he has a very good success rate.