If you hover over the task and go to the notes section, you will see when it was added. Unfortunately, there's no way to see when it was last modified, unless of course you modify it by adding notes in which case you would see the date and time of the last note.
Would you know how else an application can do a 'sync' between todoist and itself, if a last_modified metadata is not provided by the API? It seems like a common issue that developers would run into, as it would be hard to determine whether the local or remote should take precedence.
I would be interested in a recommendation from the todoist development team.
There are a couple of sync properties that is purposed to implement syncing between a client and the server, and that is "seq_no" and "seq_no_global". Storing locally these properties and then sending them when syncing with the server, one can get only those objects that were updated on the server.
These are documented here:
Also, note that right now these 2 properties hold the same value and they are increasing globally for all users, but soon, one of them will be user specific, which will simplify this situation.
But we're also working on a new feature that will make it possible to know when a task has been last modified, among other things. For this reason we are not planning on adding such a "last_modified" field in the items' properties. Please be patient and we hope that we will have this functionality quite soon.