Low complexity implementation of a small blocksize cipher (< 64 bit)
This will probably be OK.  It does have some non-trivial side effects/caveats:


The effective key length is reduced to 86 bits.  Only the low 22 bits of each of the 4 key words will matter, so only 88 bits of the key material are relevant.  Then, there are known equivalent-key properties of TEA that further reduce the effective key length to 86 bits.
A 44-bit block width is uncomfortably narrow.  Most modes of operation will have security weaknesses if you encipher more than about $2^{22}$ blocks of data.  Even if you encrypt a fraction of that much data, there's still a chance of problems: if you encipher $b$ blocks of data, there's about a $b^2/2^{45}$ chance of some sort of problem.
Due to the equivalent keys, TEA is not suitable for building hash functions.


Have you considered using something other than a block cipher?  Maybe a stream cipher?  What are your needs?