Mechanically altered seems to be the stage in food prep before it is pureed. It is basically mashed down to a pulp or an unappetizing lump on a plate. He was eating from a pretty typical menu at the assisted living on Saturday afternoon, with some things cut up into "finger food" sized pieces. The lumps of mush on his plate are not helping with his attitude regarding having to move to a nursing home.
It could be that they are being cautious with a new resident and will alter his diet plan as they observe how capable he is, keep your eyes open and bite your tongue for the first few days then ask for a meeting with whoever is in charge to bring up your concerns.
The home must do several things:
Offer the refused item more than once;
Explain the consequences of what may happen if the resident refuses (he may chock);
And they must document in his medical record the refusal.
Once this is done they are required to honor the refusal!
If I were you I would tell the home that you are aware of your dad's "right to refuse" and let them know that he is exercising his right! If you continue to have a problem let me know and I will post the regulation on this site.
If a senior is unable to manage normal self-feeding, chewing, or swallowing, then they are ordered a "mechanical soft diet." This includes things that are easy to chew such as macaroni & cheese, hamburger, or finger-foods. This is an appropriate diet for a person with any impairment at all.
Either you or your father may be "overestimating" his ability to chew or self-feed so-called "normal" foods. I don't know how old he is - but do you honestly think that he can manage to eat a T-bone steak?