Considering that Grid-fire is a weapon, and that the Culture is far, far ahead of the TSAB, that'd at least will make the TSAB very wary of the Culture.
On the otherhand, the TSAB does deploy Arc In Ciels as weapons, so I don't think the issue of using Dimensional Dislocations as weapons of war by itself would horrify the TSAB. Given that the Culture probably doesn't use Grid-fire casually, I'd imagine that the TSAB will lean towards being both wary but also impressed.
Let's face it. The Culture is far, far ahead of probably even Al-Hazard. I'd think it'll be what the Minds plan for the TSAB that will be the main issue of any first contact, what the TSAB thinks of the Culture would only be a lesser issue subsumed in that main issue. What I'd imagine would be that Contact would infiltrate TSAB society and introduce Culture Level A.I technology. Imagine Intelligent Devices with ten times Reinforce Zwei's intellect and processing capacity. Imagine Devices being used to run entire planets.
Another technology the Culture would arguably eagerly share would be Orbital Technology, which certainly would revolutionize the TSAB thoroughly. On the other hand, Culture Minds would also be eagerly analyzing and studying TSAB Magic.
Still, imagining Nanoha as a Special Circumstances Agent is an entertaining mental exercise that might spawn fanfictions.... and in the Culture, NanohaX Fate is a certainty- I'd imagine they would follow the Culture tradition of double pregnancies for both parties who are deeply in love with one another.
And then, Hayate Yagami as a referral, and Rein Eins as a very ancient Eccentric Culture Mind whose sanity was only recently restored....
Was thinking about a different angle on the Culture-Nanoha crossover... What if using Gridfire does the same thing as what the TSAB considers a dimensional dislocation? Would the TSAB be horrified that the Culture does it so casually, or impressed that they can create and fix dislocations at will?