From reading your code in Ordering of links at node - #6 by Maria I think it would be useful if you turned on having the GraphLinksModel maintain a unique key for each link data object in the GraphLinksModel.linkDataArray, just like the key that is always maintained by all Models for each node data object in the Model.nodeDataArray.
You can do that by setting GraphLinksModel.linkKeyProperty to the name of the property on the link data object that you want to hold the key value. Typically you would call it “key” or maybe “id”.
That way you can depend on the “key” for identifying or finding particular links, rather than doing a linear search through all links for one that has the desired “from” node key and the “to” node key. Just call GraphLinksModel.findLinkDataForKey or GraphLinksModel.containsLinkData, depending on whether you have the key or the reference to the link data object.
Then when a link is deleted you just have to save the key, not a bunch of values that hopefully uniquely describe the link. This is also demonstrated by the Model.toIncrementalJson method Model | GoJS API which produces a summary of the effects of a Transaction.