They dug a 10 foot trench across my lawn and installed what seems to be a permanent plastic white box that's 2.5 feet by 1.5 feet in the middle of my lawn. Bell didn't touch my lawn at all when they installed Fibre. Is there anything I can do? If not, I'm considering removing it myself and dealing with whatever the consequences.
The box is probably located on the part of the lawn that is not yours, but rather owned by the city/town. The first couple of metres from the road/sidewalk usually are, but it can depend on the width of the road, etc. If you have the survey of your home, it's usually shown there.
I wouldn't interfere with this box if I were you. Is the box at grade level or does it stick up? Bell may have put their access point grade level box(es) on a different property, but they usually have one too. Bell recently put fibre in our area and they "tunneled" most of the fibre, but every few homes there's a 1' x 1' grade level box with a bigger one roughly on each block requiring additional disruption of the yard. There's not much you can do about this as it's not your property.
The key problem here is knowing exactly where your property survey bars are located and where the property easements are located. Those easements allow utilities and companies such as Rogers access to your property for the purposes of installation and maintenance. If the trenching and box are within the easement, there's probably little that you can do. If the box is outside of the easement, then Rogers would have required your permission to install the box, and if that's the case, then you probably have every right to ask for its removal. I wouldn't recommend removing the box yourself. You should review your property plan and if necessary, have your property surveyed in order to have that survey on hand, with easements indicated on the plan. Next step would be a discussion with Rogers, possibly with appropriate legal representation for you.