Step 1: Understand the question.
We must pick the two incorrect statements about recombinant DNA tools. So we look for the statements that are false.
Step 2: Check statement A.
A says alien DNA can be joined to the origin of replication. This is correct, because a piece of foreign DNA must be linked to an ori so it can copy itself inside the host. A is true, so it is not an answer.
Step 3: Check statement B.
B says DNA ligase can act as a restriction enzyme. This is wrong. Ligase joins DNA pieces together, while a restriction enzyme cuts DNA. They do opposite jobs. So B is incorrect.
Step 4: Check statement C.
C says each restriction endonuclease recognises a specific palindromic sequence. This is correct. These enzymes read a particular palindrome and cut there. C is true, so it is not an answer.
Step 5: Check statement D.
D says exonucleases cut at a specific position of DNA. This is wrong. Exonucleases trim nucleotides from the ends, while it is the endonucleases that cut at specific internal sites. So D is incorrect.
Step 6: Pick the incorrect set.
The two wrong statements are B and D.
\[ \boxed{\text{B and D}} \]