What is Pseudopalindrome?
In DNA there are four nucleotides or "bases", each of which can be matched with a complementary base on the partner chain in the double helix. Thus:

Adenine (A) and Thymine (T) are complementary and Cytosine (C) and  Guanine (G) are complementary.

So, a nucleotide sequence is said to be a palindrome if it has an even number of base pairs and is equal to the reverse of its complementary sequence.

For example, in a single strand of DNA the sequence of bases CCATTAATGG is palindromic because the sequence of bases in the complementary strand is GGTAATTACC, its reverse.

A pseudopalindrome is a DNA sequence with an odd number of base pairs yielding a symmetrical complement except at the central base-pair. For example, the DNA sequence ACCTGGT is pseudopalindromic, because its complement on the other strand is TGGACCA, which is its reverse except for the central element.

[There may be some confusion in the literature. The example cited in the question, GATC, is a palindrome, having CTAG as its complement, not a pseudopalindrome.]