I would have thought that although it is rated with dual voltages, it could still be used with an inverter.
It is common for three phase motors to be capable of being wired either star or delta. The impedance of the winding is different in either configuration. The rating plate should say if the rating is star or delta. If it does not, you would probably assume that the rating is for delta. This is how larger/older motor rating plates work, to allow for star/delta starters.
In your case the label inside the connection cover implies that the two voltages on the rating plate are for delta and star respectively. I'd say that you can use that motor with either a three phase or a single phase input inverter.
It does depend very much on what inverter you obtain to use with it. Generally an inverter with a single phase input will only have a fairly small output voltage rating. A three phase to three phase inverter would normally have a much higher output voltage rating. This is not a rule, just an observation.
To compensate and get broadly equivalent ratings from a motor at different voltages you would wire 240V delta and say 415 star. If you just want the maximum from the motor, wire delta whatever the supply. If you want efficiency and/or low inrush wire star.
There is absolutely no reason not to use a motor like yours with an inverter. You should do some simple experiments however. Get a current clamp and verify the rating plate data. You can also get thermistor protection relay packages from people like ABB automation. These can act to stop the motor in thermal overload conditions. That might be quite important with a fully sealed motor, like this. Obviously it must have poor airflow.
The connections you will have to buzz out. It looks to me like someone has written the terminal numbers on the wires. Check them obviously, but there is no reason not to use 10A marathon/choc block inside the box to make connections.
You should expect it to work out such that low voltage is the delta connection and high voltage is star connection. If it doesn't something is up.