If you wish to check if the file links of an item are up-to-date, using the API, then you can make use of the ItemFileLinkState property for that particular Item. So for e.g:
try {
Item item = connection.WebServiceManager.ItemService.GetLatestItemByItemNumber("10001");
PropDef[] propDefs =
connection.WebServiceManager.PropertyService.GetPropertyDefinitionsByEntityClassId("ITEM");
PropDef propdef =
propDefs.Where(s => s.SysName == VDF.Vault.Currency.Properties.PropertyDefinitionIds.
Server.ItemFileLinkState).First();
PropInst prop =
connection.WebServiceManager.PropertyService.GetProperties("ITEM",
new long[] { item.Id }, new long[] { def.Id }).First();
var value = prop.Val; }
This would return 3 possible values - 0, 10 and 20, which basically means: 0 – “Out of Date “; 10 – “Current”; 20 - "No links".