"to what degree" is a question phrase, so you can't have "consider that" since "that" creates a non-question clause. Also, a question phrase tends to go to the beginning of the clause. You might rewrite your sentence as: 1. The author fails to consider to what degree the level of these Alpha’s former workers and their specialty can help the company. (But it still sounds strange. Is "Alpha" a company name? If so, you can rewrite it as follows) 2. The author fails to consider to what degree these former Alpha employees can help the company with their specialties.

‘To what degree’ is usually part of a question, e.g ‘to what degree are these workers of benefit to the company?’, or ‘to what degree has output been affected by the strike?’. Something more similar to your sentence might be - ‘has it been considered to what degree the loss of the specialities and expertise of former workers has affected overall growth (of the company etc)?’

The author fails to understand that to what degree the level of........

It basically means, "to what level" or "to what amount" or its like asking for the listener to explain "how helpful can this person be?" "To what degree can this person be of service to me?"

The context of your sentence is difficult to follow, so it appears to be grammatically incorrect. However, I can try and explain the usage of the phrase "to what degree" for you.