The sample should have had arrived at UK on last Monday. 請問這句話的文法有錯嗎？為何have had後面又有過去分詞？？

沒有錯！

只是我們中文人學英文一般學藝不深，學校老師也曾說過英文動詞中這種"完成式"是最難學的，再加上假設性的修辭，並且看來是強調送貨"過了期"/延誤了，對方才會用這複雜的句式。

這動詞should have had arrived拆解如下：
arrive是基本動詞=對方想表達的主題是貨物的"送達"/"到達"情況；
have had可看成"已經"(have)的現在完成式，意思是想表達基本動詞(arrive)應該是"已經"have arrived的過去情況了，現實卻是"未完成"，這是修辭或情緒的表達時間過期了。
推前一個should have是表達"原意應該是"但現在卻不是的修辭。例如you should have done your homework.意思是你"應該"做好了功課，但實際上你"沒有"。這例句用"簡單完成時態"是按做功課這動作/行為的重要性而設。對比問題的句子，作者加了should have had是強調"arrive"這行動是"應該已經發生了的，但實際上卻沒有發生。例如這例句的說話不是你媽跟你在家說，而說的是你的老師在學校要交功課的時間：她/他的說法可能是：You should have had done your homework because now you will get "zero" mark for this assignment.意思是由於你沒有按時"已經"完成功課(字面的意義是:你現在沒有(你應該已經完成的)功課交)，所以你現在要得零分了。

這是一種強調語氣的寫法。

The sample should have had arrived----
=should have (arrived)
=had arrived--->passive in Main Clause
If UK last Monday(had not been chopped)
=had not been post-delayed
=post- delayed---> unfinished sentence to If Clause
=If Clause.

1. 我同意您的想法，也認為had應刪掉。
2. 又，on last Monday的on也可刪掉。

文法當然有錯!
原句的意思應該是: 如一切正常，樣品應在上週一已經抵達。

We can also the modal "should have + past participle" to talk about something that, if everything is fine, we think has already happened. (but we're not certain that everything is fine)

===> The sample should have arrived at UK by last Monday.