How did the silent 't' come into all these 'tch' words?

I'm curious as to how so many words with the 'ch' sound have the silent 't' in them. Catch, itch, retch, hatchet, botch etc. The list is huge.

They all have different origins, and yet they have the silent 't'. But words like achieve, lecherous, spinach don't have the silent 't'.

Can anyone see any phonological patterns that might have led to this?

It seems to me that the 'tch' behaves in English spelling the way a doubled consonant would, and the 'ch' the way a single consonant would. That is, 'tch' is more likely to occur after short vowels, so you see patch, botch, and crutch, but beach, roach, and pooch. As with any English spelling rule, there are numerous exceptions.

The words you mention have been spelt in many different ways over the centuries. To take just two examples, hatchet has also appeared as hachet, acchett, hachit, hachytt, hachette and hatchette and achieve as acheui acheeve, achyeue, atcheue, acheue, acheve, achieue, achyue, achieve, achiue, ascheve, atcheive, atchive, atchieue, atchiue, atchive, atchieve, acheive, atcheeue; acheive, acheue, atcheve, achieve and acheive. Make of that what you will.