1.In both 1.0 and beta version of Graph, ListItem delta query supports the $select, $expand, and $to OData query parameters. It does not support filter parament.
2.I can reproduce the issue, OData query parameters do not work with @odata.deltaLink in the Graph explorer.
3.Here are example codes to get ListItem delta from local.
var listItems = await graphClient.Sites["xxxxxxxx"].Lists["xxxxxxxxxx"].Items.Delta.WithUrl("https://graph.microsoft.com/v1.0/sites/xxxxxxxx/lists/xxxxxxxx/items/delta?$deltatoken=xxxxxxxxx").GetAsDeltaGetResponseAsync();
foreach (var listItem in listItems.Value)
{
Console.WriteLine("id: " + listItem.Id + "\n" + "type: " + listItem.ContentType);
}
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