We went in our back garden today and noticed some damage to rose bushes.
We saw ladder damage to our lawn.
Firstly, you need to document this damage if you haven't already. Secondly, what kind of damage are we talking? If the damage is significant (eg, the rose bushes need to be replaced, the lawn repaired) then you are entitled to have it put right.
Your first port of call should be a simple conversation with your neighbors, informing them of the damage done. Ideally they should instruct their contractor to make it right.
They then exit again by our door, but one stops, looks through the door window and tries the handle, several times.
In order for the offence of attempted burglary to be committed, there must be evidence of intent to steal/cause damage. Trying a door handle, in the middle of the day, at a property you're working adjacent to, may not be evidence enough for the police to investigate, and almost certainly wouldn't be enough to charge.
Our neighbours did not ask our permission and have not mentioned a thing to us.
If your neighbors have told the builders to access their work via your property, that's naughty.
However that's an assumption. They may have, they might not have mentioned anything or they might have explicitly instructed the builders not to access your land, and been ignored.
Another neighbour has told me she messaged the neighbour to say the builders were on our land, so they knew.
Did your neighbors respond to the message? If not, you have no idea when this message was seen, or if they raised it with the builders or not.
What should I now do?
As above, talk to them! They presumably have no idea that your lawn/roses were damaged. They may be mortified and get things resolved immediately. They're obviously not responsible for the builder checking your door, but they may appreciate the heads-up.
They don't seem to have done anything 'awful' in this scenario as of yet, so I'm guessing the thread title hints at ongoing issues?