Trans World Entertainment Corporation, which owns the Record Town and Saturday Matinee retail chains, announced that since sales of up to one-fourth of its stores are poor, they will be closed.
C. it was closing up to one-fourth of its stores because of poor sales
I do not think that dropping of 'that' is an issue here. The grammar custom in written and spoken language is that one can drop the relative clause connector 'that' even in reported speeches if a noun or noun phrase follows the word. Example: 1. On reaching the Airport, I realized (that) I had not brought my passport.
2. The minister gloated (that) the country ultimately got a well-qualified and deserving Judge for the top court.
3. The priest realized quite late (that) his preaching made people snooze
In all the above cases, we may see the dropping of the relative clause connector 'that' does not make any difference.
4. If you want an official example, then this is the one. But, there are many more I am sure.
However, one cannot drop 'that' if there is only a verb after it. Because 'that' in such cases acts as a subject of the verb and as such by dropping it you might end up in a subject -less clause Example
1.
MGMAT sells some books that are called five-pound books
2. On reaching the Airport, I could not spot my passport that is required for even entry into the premises.
Try dropping 'that' in these cases, you will find that those clauses do not mean sensibly.
We can confidently pass C.