"they could to restore services, ..."

"But if local and federal authorities wanted affirmation that they were seen to be doing the best they could to restore services, then it came late on Thursday when the only bone of contention on the news radar was the wisdom of a decision by organisers of Sunday's New York City Marathon to go ahead with the event which is expected to draw a field of more than 40,000 and traditionally pulls as many as a million spectators."

More: Tragedy through the eyes of ordinary people

Can we use infinitive after modal verbs?

You have to separate the words differently. It is not saying "they could to restore service." It is saying they did the best they could. To restore service.

Is it a trick? Did I fall into the trap of thinking that the preposition to must not come after model verbs? Thank you, SoothingDave, for your precious help.

Sometimes "could" is just the simple past tense of "can," and not a modal verb.

'Can', except when it is used in the sense of 'preserve in a can' (past tense 'canned'), is always modal; 'could' is always modal. The infinitive may be understood - "Please come if you can (come)". In OD's original sentence, 'to' can be understood as 'in order to'.