Why would decreasing ionic strength of buffer disrupt hydrogen bonds
At high ionic strength, the poly-A tails of mRNA bind oligo-dT that is covalently attached to beads in a column (source). The binding interaction is based on base stacking and hydrogen bonding. When you decrease the ionic strength, the repulsion between the (negatively charged) phosphate groups becomes stronger (is shielded less by counter ions), lowering the binding strength to the point that the mRNA elutes.

The length of the oligo-dT on the beads is chosen such that the mRNA binds sufficiently strong at high ionic strength, but is released at low ionic strength. The appropriate length of oligo-dT is probably on the order of 8-10 nucleotides.


  decreasing the ionic strength of the buffer so that the hydrogen bonds will be disrupted


This statement does not capture the situation accurately. What is really being disrupted is the overall binding of mRNA to the beads. The hydrogen bonds, as short range interactions, should not be directly affected by ionic strength. The stacking interactions might weaken with decreasing ionic strength. Long range ionic interactions, however, are significantly weakened by increasing ionic strength because counter-ions bound to the phosphate backbone will strongly shield the ionic interactions (water also shields it compared to vacuum or non-polar solvents). In this case, the ionic interactions are repulsive, so binding will get weaker at low ionic strength because that is when the repulsive interactions are strongest.